Question

In an A.P., a = –3 and S\(_{17}\) = 357. The value of a\(_{17}\) is

• A. 47
• B. 39
• C. 45
• D. 42

Hint:

Using the formula \(S_n = \frac{n}{2}(a + a_n)\) is much faster than using \(S_n = \frac{n}{2}[2a + (n-1)d]\) because it avoids having to find the common difference \(d\) first!

Answer 1

The Correct Option is C

Step 1: Find the common difference first.
Using $S_n = \frac{n}{2}[2a + (n-1)d]$ with $n = 17$, $a = -3$, $S_{17} = 357$:
\[ 357 = \frac{17}{2}[2(-3) + 16d] \]
Step 2: Solve for d.
\[ 42 = -6 + 16d \implies 16d = 48 \implies d = 3 \]
Step 3: Find the 17th term directly.
\[ a_{17} = a + 16d = -3 + 16(3) = -3 + 48 = 45 \]
\[ \boxed{a_{17} = 45} \]