NIMCET 2026 — Reasoning PYQ

This is an Arithmetic Progression (AP) where the first term $a=72$ and the common difference $d=69-72=-3$.

1. Find the number of positive terms ($n$):

The $n^{th}$ term formula is $a_n=a+(n-1)d$. We need a_n > 0:

72 + (n - 1)(-3) > 0

72 - 3n + 3 > 0

75 > 3n \implies n < 25

So, there are $24$ positive terms.

2. Calculate the sum of the first $n$ terms:

The formula for the sum of an AP is $S_n=\frac{n}{2}[2a+(n-1)d]$:

$$S_{24}=\frac{24}{2}[2(72)+(24-1)(-3)]$$

$$S_{24}=12[144+23(-3)]$$

$$S_{24}=12[144-69]$$

$$S_{24}=12[75]$$

$$S_{24}=900$$

The maximum sum of terms is (c) 900.