Question

The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :

• A. 10
• B. 5
• C. 6
• D. 13

Answer 1

The Correct Option is B

Let the AP have $n$ terms, with first term $a = 9$ and common difference $d$.
First three terms: $a, a + d, a + 2d$
\[\text{Sum} = 3a + 3d = 30 \implies d = 1\]
Last three terms: $a + (n - 3)d, a + (n - 2)d, a + (n - 1)d$
\[\text{Sum} = 3a + 3(n - 3)d = 36 \implies 27 + 3(n - 3) = 36 \implies n = 6\]