Question

how many terms of the series 1 + 4 + 16 make the sum 1365​

Answer 1

Answer:

Step-by-step explanation:

The series is a geometric progression as r = common ratio =  4 / 1 = 16 / 4 = 4

Therefore r = 4 and r > 1

Sum of a geometric progression, when r > 1 = a($r^{n}$ - 1) / r - 1

Where a  = first term, r = common ratio and n = number of terms

Therefore 1365 = 1 * ($4^{n}$ - 1) / (4 - 1)

1365 * 3 = $4^{n}$  - 1

4095 + 1 = $4^{n}$

or $4^{n}$ = 4096

4096 = $4^{6}$

Therefore $4^{n}$ = $4^{6}$

or n = 6