Question

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

Answer 1

Answer:

16 terms

Step-by-step 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