Question

Find the sum of the Geometric series 3 + 6 + 12 + …….. + 1536

Answer 1

3 + 6 + 12 + …. + 1536

a = 3, r = ${\displaystyle \frac{6}{3}}$ = 2

t_n = 1536

a.r^n–1 = 1536 ⇒ 3(2^n–1) = 1536

2^n–1 = ${\displaystyle \frac{1536}{3}}$ ⇒ 2^n–1 = 512

2^n–1 =  2⁹

∴ n – 1 = 9

n = 9 + 1 = 10

Number of terms = 10

S_n = ${\displaystyle \frac{\text{a}({\text{r}}^{\text{n}}-1)}{\text{r}-1}}$

S_n = ${\displaystyle \frac{3(2^{10}-1)}{2-1}}$

= ${\displaystyle \frac{3(1024-1)}{1}}$

= 3 × 1023

= 3069

∴ Sum of the series is 3069