Fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?
Show Hint
- 7
- 64
- Cannot be determined
- 56
The Correct Option is D
Solution and Explanation
For an AP with first term \(a\) and common difference \(d\), \(S_7 = \frac{7}{2}\,(a_1 + a_7)\).
Step 2: Use the middle term:
The fourth term is the middle one of the seven terms, so \(a_1 + a_7 = 2a_4\) (for example, \((a_4-3d) + (a_4+3d) = 2a_4\)). Hence \(S_7 = \frac{7}{2}\times 2a_4 = 7a_4\).
Step 3: Substitute:
\(a_4 = 8\), so \(S_7 = 7 \times 8 = 56\). The answer does not depend on \(a\) or \(d\) separately, so it can be determined.
Final Answer:
The correct option is (4): 56.
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