Question

Find the first term of the G.P. whose common ratio 5 and whose sum to first 6 terms is 46872

Answer 1

Common ratio, r = 5

S₆ = 46872

∴ ${\displaystyle \frac{\text{a}({\text{r}}^6-1)}{\text{r}-1}}$ = 46872

⇒ S₆ = ${\displaystyle \frac{\text{a}(5^6-1)}{5-1}}$ = 46872

⇒ a = ${\displaystyle \frac{46872\times 4}{[25\times 25\times 25-1]}}$

⇒ a = ${\displaystyle \frac{187488}{15624}}$ = 12

⇒ first term = 12