Q.Find the sum of the first 6 terms of the GP $2, 6, 18, \ldots$

This GP has $a=2$ and $r=3$, so the standard sum formula for $r \neq 1$ applies for the first 6 terms.

Given: GP $2, 6, 18, \ldots$, find $S_6$.

Step 1 — Identify $a$ and $r$: $a=2$; $r = 6/2 = 3$ (check: $18/6=3$ ✓).

Step 2 — Apply the formula: $S_6 = \dfrac{a(r^6-1)}{r-1} = \dfrac{2(3^6-1)}{3-1}$.

Step 3 — Compute $3^6$: $3^3 = 27$; $3^6 = 27^2 = 729$.

Step 4 — Substitute and simplify: $S_6 = \dfrac{2(729-1)}{2} = \dfrac{2 \times 728}{2} = 728$. …

Arithmetic slip in computing $3^6$ (often mistaken for $3 \times 6 = 18$) — always compute powers by repeated multipli …