Question

Find the sum of the given series: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192?
1. 17180
2. 18150
3. 15750
4. 16380

Answer 1

Correct Answer - Option 4 : 16380

Given:

G.P. Series: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

Formula Used:

T_n = ar^(n-1)

S_n = a(rⁿ-1)/(n-1)

Calculation:

GP Series: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

T_n = ar^n-1

⇒ 8192 = 4 × (2)^n-1

⇒ 2048 = 2^(n-1)

Therefore,

⇒ 2¹¹ = 2^n-1

⇒ (n – 1) = 11

⇒ n = 12

Sum of series (S) = a(rn- 1)/(n - 1)

⇒ S = 4 × (2¹² - 1)/ (2 - 1)

⇒ S = 4 × (4096 - 1) = 4 × 4095

∴ S = 16380