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:

Use \(S_n = \frac{n}{2}(a + l)\) instead of \(S_n = \frac{n}{2}[2a + (n-1)d]\) when the question involves the last term directly. It saves a lot of algebra.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The sum of the first \(n\) terms of an Arithmetic Progression can be calculated using the first and last terms.
Step 2: Key Formula or Approach:
Sum formula: \(S_n = \frac{n}{2}(a + l)\), where \(l\) is the \(n\)-th term.
Here, \(n = 17\), \(a = -3\), \(S_{17} = 357\). We need to find \(l = a_{17}\).
Step 3: Detailed Explanation:
\[ 357 = \frac{17}{2}(-3 + a_{17}) \]
Multiply both sides by 2 and divide by 17:
\[ \frac{357 \times 2}{17} = -3 + a_{17} \]
\[ 21 \times 2 = -3 + a_{17} \]
\[ 42 = -3 + a_{17} \]
\[ a_{17} = 42 + 3 = 45 \]
Step 4: Final Answer:
The value of \(a_{17}\) is \(45\).