Q.A person saves ₹500 in the first month and increases the monthly saving by ₹100 every subsequent month. Find the total amount saved over the first $10$ months.

Monthly savings form an AP with $a = 500,\ d = 100,\ n = 10$; apply the sum formula.

The monthly savings run $500, 600, 700, \ldots$ — an AP with $a = 500$, $d = 100$, $n = 10$ months (a fixed amount added each month signals an AP, not a GP).

Apply $S_n = \dfrac{n}{2}\big[2a + (n-1)d\big]$:

$S_{10} = \frac{10}{2}\big[2(500) + (10-1)(100)\big] = 5\big[1000 + 900\big] = 5(1900) = 9500.$ …

Treating the increase as a percentage (a GP) instead of a fixed rupee amount (an AP) — the phrase "increases by ₹100" is a fixed amount, s …