Find the third term of a G.P. whose common ratio is 3 and the sum of whose first seven terms is 2186.

Given, r = 3 and S₇ = 2186.

Using formula $S_n = \dfrac{a(r^n - 1)}{r - 1}$ we get,

$\Rightarrow S_7 = \dfrac{a(3^7 - 1)}{3 - 1} \\[1em] \Rightarrow 2186 = \dfrac{a(2187 - 1)}{2} \\[1em] \Rightarrow \dfrac{2186a}{2} = 2186 \\[1em] \Rightarrow a = 2. \\[1em]$

∴ Third term = a₃ = ar² = 2(3)² = 18.

Hence, the third term of the G.P. is 18.