Question

Number Series 1,4,15,64,325,_

Answer 1

it begins with 1

1*2 +2 =4 Second number

4*3+3=15 Third number

15*4+4=64 Fourth number

64*5+5=325 Fifth number

Answer 2

Given,

Number Series 1,4,15,64,325,_

To Find,

The next term =?

Solution,

We can find the next term of the given series as follows:

Taking the first term,

$1 = (0 * 1) + 1$

Taking the second term,

$4 = (1 * 2) + 2$

Taking the third term,

$15 = (4 * 3) + 3$

Taking the fourth term,

$64 = ( 15 * 4) + 4$

Taking the fifth term,

$325 = (64 * 5) + 5$

Clearly, each term is equal to the previous term multiplied by n and then added to n

$T_{n} = (T_{n - 1} * n) + n$

Where, $n = 1, 2, 3, 4, 5,$ so on or the position of the nth term.

Now,

The sixth term will be equal to the fifth term multiplied by 6 and then added to 6.

$T_{6} = (325 * 6) + 6 = 1956$

Hence, the number series will be 1,4,15,64,325,1956.