Question

What is the next term of the number series 4,16,36,64...?

Answer 1

Answer : 100

Explaination :
____________

4×(0+1)= 4×1 = 4

4×(1+3) = 4×4 = 16

4×(4+5) = 4×9 = 36

4×(9+7) = 4×16 = 64

4×(16+9) = 4×25 = 100

So, the next term will be 100

Answer 2

The next term of the number series 4 , 16 , 36 , 64 , . . . is 100

Given : The number series 4 , 16 , 36 , 64 , . . .

To find : The next term of the number series

Solution :

Step 1 of 3 :

Write down the given number series

The number series is 4 , 16 , 36 , 64 , . . .

Step 2 of 3 :

Find the patten of the number series

1st term = 4 = 2²

2nd term = 16 = 4²

3rd term = 36 = 6²

4th term = 64 = 8²

Step 3 of 3 :

Find next term of the given number series

The numbers 2 , 4 , 6 , 8 form arithmetic progression with

First term = 2

Common Difference = d = 4 - 2 = 2

So the next of the AP 2 , 4 , 6 , 8

= 8 + d

= 8 + 2

= 10

Hence next term of the number series

= 10²

= 100

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