Question

Find the total number of terms.32,256,2048,16384,......,2⁵⁰

Answer 1

16 terms

Explanation:

32,256,2048,16384,......,2⁵⁰

32=2⁵

256=2⁸

2048=2¹¹

16384=2¹⁴

2⁵, 2⁸, 2¹¹,2¹⁴, ….,2⁵⁰

`t_(1)`=2⁵;
`t_(2)`=2⁸

r=2⁸:2⁵=2³

`t_(n)`=
`t_(1)`*
`r^(n-1)`

2⁵*
`2^(3(n-1))` =2⁵⁰

5+3(n-1)=50

3n-3=45

3n=48

n=48:3

n=16

So, 16 terms