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

∴ `("a"("r"^6 - 1))/("r" - 1)` = 46872

⇒ S₆ = `("a"(5^6 - 1))/(5 - 1)` = 46872

⇒ a = `(46872 xx 4)/([25 xx 25 xx 25 - 1])`

⇒ a = `187488/15624` = 12

⇒ first term = 12