Question

How many terms of the series $2+6+18+$...must be be taken to make the sum equal to $728$?

Answer 1

$a=2$

$a_n=728$

$r=\frac{6}{2}=3$

Sum$=\frac{a(r^n-1)}{r-1}$

$728=\frac{2(3^n-1)}{3-1}$

$728+1=3^n$

$729=3^n$

$\therefore n=6$.