Online Assignment help - from India

Finding the n th term in a sequence

noreply@blogger.com (Sridhar Venkatesh) — Fri, 15 Mar 2013 17:47:00 +0000

We encounter situations to find the n^th term of a series that is neither in arithmetic progression nor in geometric progression, and here we use the below simple technique to figure out the n^th term.

Say we have a sequence in which the nth term is to be figured out. If the sequence of numbers are in Arithmetic progression or Geometric progression or Harmonic progression we have direct formula to find the n^th term. But if the series follows none of the above progressions, even then we have a simple method to calculate the n^th term applying basic mathematical tools.

Say the sequence is

10 12 16 22 30 . . . . .

We shall consider the general expression aN²+ bN + c

Where N denotes the term number and a,b,c are constants, now we can generate equations using the general expression as shown below:

Equation 1 : Put N = 1 in general expression and equate it to 10 ( first term ) a+ b +c = 10

Equation 2 : Put N = 2 in general expression and equate it to 12 ( second term ) 4a+2b+c = 12

Equation 3 : Put N = 3 in general expression and equate it to 16 ( third term ) 9a+3b+c = 16

Now solving the above three equations we obtain the values of constants a,b and c.

Solving of equations may be done using matrices or linear equation formula.

By elimination method Eliminating c in Equation 1 and 2 (Subtracting eq 2 from eq 1) we get 3a + b = 2

Again Eliminating c in Equation 2 and 3 (subtracting eq 2 from 3) we get 5a +b = 4

Now solving the equations thus obtained, 3a+b= 2 and 5a+b=4.

Eliminating b from below equations ...

5a + b = 4

3a + b = 2

We get 2a = 2 and a =1 from the above equations hence finding b value from the same equation b = -1

and similarly c = 10

The general expression becomes N²-N + 10

and thats the nth term of the given series.

The same way one can find the n^th term for any series.

Pal Multiplication. . .

noreply@blogger.com (Sridhar Venkatesh) — Mon, 11 Feb 2013 15:01:00 +0000

Wanna multiply 99 with another number, do it simpler as shown below

Any two digit number can be multiplied with 99 in no time. Let us look this with the help of a simple example.

Say you want to multiply 54 and 99. All you need to do is simple subtraction.

We know that : 56 X 99 = 5544 ( by usual multiplication )

Step 1 : Reduce 1 from the number to be multiplied with 99 and find the answer. 56 -1 = 55.

Step 2 : Subtract the obtained answer from 99 and calculate the balance. 99- 55 = 44

Step 3 : Place both answers of step 1 and 2 side by side in order, you end up with the product easily.
Answer = 5544

Here the answers of step one and two are treated as friends and they sit adjacent to each other always and so this multiplication got the name 'pal multiplication'. That was cool ... :)

Lets look at another case, say 21 is to be multiplied with 99

Firstly subtract 1 from 21. 21-1 = 20.
Now subtract 20 from 99. 99-20 = 79
Product = 2079 ; Also we know that 21 x 99 = 2079.

NOTE : Please do remember that this simple technique is useful in calculating 2 digit numbers only.

Special Numbers

noreply@blogger.com (Sridhar Venkatesh) — Sat, 09 Feb 2013 18:14:00 +0000

Special numbers have always been identified and appreciated by mathematicians over the years. They usually exhibit peculiarity which highlight their presence in manipulation. By chance we might have seen such numbers in our day to day practice, which have not come into light. Now we shall look at numbers of the same sort.....

376 - Genetic Multiplication

Number 396 is so special that, when we multiply and number ending with 376 ( both multiplier and multiplicand ) we obtain a product ending with 376.

For instance : 376 x 4376 = 1645376

376 x 8376 = 3149376

376 x 3376 = 1267376

This is like children inheriting the genes of the parents .

Magic Multiplication

The special number 8547 gives amazing results on multiplication of 13 multiples as seen below

8547 X 13 = 111111

8547 X 26 = 222222

8547 X 39 = 333333

8547 X 52 = 444444

8547 X 65 = 555555

8547 X 78 = 666666

8547 X 91 = 777777

and so on .....

Also the number 15873 gives similar results on multiplication with 7 multiples as shown ...

15873 X 7 = 111111

15873 X 14 = 222222

15873 X 21 = 333333

15873 X 28 = 444444

15873 X 35 = 555555

Reversing !! Its Ridiculous

We might have heard / seen that 1089 is such a tricky number, now we see it lively here .....

1089 + 8019 = 9108

1089 X 1 = 1089 <=> 9801 = 9 X 1089

1089 X 2 = 2178 <=> 8712 = 9 X 1089

1089 X 3 = 3267 <=> 7623 = 9 X 1089

1089 X 4 = 4356 <=> 6534 = 9 X 1089

The symbol <=> signifies reversing the digits ... This stuff seems something like our 9 table ...

Please post your queries if any.... Thanks for your interest in Math made easy...

Marshal art Multiplication

noreply@blogger.com (Sridhar Venkatesh) — Tue, 05 Feb 2013 14:14:00 +0000

:D :D There is a special number 153846 for which we have got some cheeky manipulations.

If we multiply the number by 4, the product will be 615384

If this multiplier 4 kicked the 6 from units place to the lakh's place... and so we call is Marshal Art multiplication .... Things of this kind seem funny in math, there is fun in science too :)

Half and Laugh Multiplication

noreply@blogger.com (Sridhar Venkatesh) — Sun, 03 Feb 2013 16:03:00 +0000

Now multiply any number with 5 in no time.....
Usually we take a 2 digit number and multiply by 5, end up with a solution in some time.

In another logical sense also we can find equal product saving much time.

For odd numbers :
Make half of the multiplicand and remove the point from the answer obtained

say the number is 483, we know that half of 241.5 and now removing the point we obtain 2415
also 483 x 5 = 2415

For Even numbers :
Make half of the multiplicand and put zero after the end of the answer obtained.

say the number is 626, half of it is 313 and putting a zero makes it 3130, which gives the product in a few seconds.

That was cool, I guess ........ :)

Kilo pound conversion

noreply@blogger.com (Sridhar Venkatesh) — Thu, 31 Jan 2013 03:06:00 +0000

Not to worry about conversions, After-all there is a simple logic/ trick behind it, if thats read we are done with our job....

Firstly lets discuss Kilo - pound conversion.

Say we are trying to convert 74 kilos to pounds ....

Step 1 : Multiply the kilos with 2.

Its just doubling the number of kilos 74 x 2 = 148

Step 2 : Divide the answer by 10

Now divide 148 by 10 ; 148/10 = 14.8

Step 3 : Add answers of step 1 and step 2, you end up with number of pounds (equivalent to 74 kilos)

148 + 14.8 = 162.8

Thus 74 kilos = 162.8 pounds

Our objective is to convert the kilo to pounds or vice-versa using a time effective method, with good precision.

(The answer obtained from this simple process may deviate from the exact value in small decimal values)

UP-DOWN Method for squaring a 2 digit number.

noreply@blogger.com (Sridhar Venkatesh) — Tue, 29 Jan 2013 11:26:00 +0000

Square a 2 Digit Number, for this example 47:

Look for the nearest 10 boundary

In this case up 3 from 47 to 50.

Since you went UP 3 to 50 go DOWN 3 from 47 to 44.

Now mentally multiply 44x50

The way I do it is 44x10=440;

Mentally multiply 440 x 5 = 2200

This 2200 is the FIRST interim answer.

47 is "3" away from the 10 boundary 50.

Square this "3" distance from 10 boundary.

3x3=9 which is the SECOND interim answer.

Add the two interim answers to get the final answer.

Answer: 2200+ 9 = 2209

In a critical view point, the above trick is bound to the following identity,

( x + y ) ( x - y )= X² - Y²

Wheres x is the original number and y is the up/ down correction. After getting the answer we add y^2 to normalize the answer as x^2

With practice this can easily be done in your head.

claim token : TQMU6C95ZT2K

Finger Math: Do it simpler :)

noreply@blogger.com (Sridhar Venkatesh) — Tue, 29 Jan 2013 10:51:00 +0000

The young ones find it hard to memories multiplication tables, well this will definitely seem interesting ....

To multiply by 9,try this:

Step 1: Spread your two hands out and place them on a desk / table in front of you.

Step 2: To multiply by 2, fold down the 2nd finger from the left. To multiply by 4, it would be the 4th finger and so on.

Step 3: The answer is 18 ... READ it from the one finger on the left of the folded down finger and the 8 fingers on the right of it.

This works for anything up to 9x10!

Multiply with 11 in seconds :)

noreply@blogger.com (Sridhar Venkatesh) — Mon, 28 Jan 2013 15:21:00 +0000

Its so simple... You should be able to do this one in you head for any two digit number. Try to work it out on paper before you take it into your mind.
To multiply any two digit number by 11:

Step 1 : Separate the given number as shown (say the number is 32 then, write it as 3__2)

Step 2 : You find a gap between the numbers, its been left wanted, to be filled in the next step

Step 3: Sum up the digits of the original number i.e. Add 3 and 2 the makes 5

Step 4: Fill the gap with the answer in step 3, here the gap is filled with 5. Thus the product of 11 and 32 becomes 352, and howsatt !!

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 67 ... 6__7 ... 6+7=13 ... put the 3 in the hole and add the 1 from the 13 to the 6 in to get 7 for a result of 737 ... 11 x 67 = 737

Work this on paper, practice a few examples and move on ....

Hope this was educative, catch up our updates, subscribe our RSS.

The coolest trick is here ...

noreply@blogger.com (Sridhar Venkatesh) — Mon, 28 Jan 2013 07:22:00 +0000

Write down a three digit number Each digit must get smaller as you read from left to right (eg)542.

Reverse the digits and take this number away from the original number, we get (542 - 245 = 297).

Reverse these digits and add them to the new answer (297+792= 1089).

The answer is always 1089!

Your can try this with your friends and prank them, you ll seem like a calculator for them.

Squaring became trivial :D

noreply@blogger.com (Sridhar Venkatesh) — Sun, 27 Jan 2013 12:10:00 +0000

Hello guest, A warm welcome to the 'Math made easy', hope your stay on our blog will be educative :) Happy learning :)

This being our first post we are going to look at some exiting stuff. When we call upon Math, whats so uninteresting about that, the calculation, it brings a complexity and feel like its hard, when we get away from this calc-Zombie, we are almost done and the subject goes well for us. Hence let us look at some easy and simple tricks that facilitate easy calculation, that paves the way for simple approach to questions/ problems.

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Coolest Trick :

When you encounter situations like find the square of 95 or 65 .... Its takes few seconds (at least) to calculate 95x95 or 65x65 and to report the answer. If theres a technique to get the answer for the above question with out using your pen & paper and you report the answer in 3 to 5 sec (maximum), How would that be ?? That would be amazing, Isn't it ?

Here you go with the procedure

Say you got to find the square of 95

Step 1: Leave the last digit 5, and you are left with 9 now (say a)
Step 2: Add one to the remaining number and get the answer. (Its 9+1 = 10 here; if its a then a+1 )
Step 3: Multiply the answers obtained in step 1 and 2.
Mathematically :
9 x 10 = 90
similarly for any number a x (a+1) = product

Step 5: Give the answer as 9025. This 25 is as a result of 5x5 from the last two digits in the given number.
Report the answer as the product obtained in step 4, putting 25 in the hundred's place.

Another Illustration

Square of 125:

>> Leaving behind 5, 12 is the number
>>Now, 12+1 = 13
>>Thus on multiplication : 12 x 13 = 156
>>Hence the square of 125 = 15625

This way get the square of any number that ends with 5. Hope that helps you. Please drop us your comments .