Question

Find the number of terms in the following G.P.

4, 8, 16, …, 8192?

Answer 1

4, 8, 16, …, 8192

Hint:
2	2048
2	1024
2	512
2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

a = 4

r = `8/4` = 2

t_n = 8192

t_n = ar^n–1

8192 = 4 × 2^n–1

4 × 2^n–1 = 8192

2^n–1 = 2048

2^n–1 = 2¹¹

n – 1 = 11

n = 11 + 1 = 12

∴ No. of terms = 12