What is the sum of the first 13 terms of the AP 9, 16, 23, ...?
Answer and explanation
Correct answer: 663
The sequence is an AP because consecutive terms differ by the constant amount d = 16 − 9 = 7. Thus a = 9 and n = 13. Use S_n = n/2[2a + (n − 1)d]: S_13 = 13/2[2(9) + 12(7)] = 13/2[18 + 84] = 13/2 × 102 = 13 × 51 = 663. Hence option C is correct. An equivalent check uses the last term: a_13 = 9 + 12 × 7 = 93, so S_13 = 13/2(9 + 93) = 663. The other options arise from an incorrect difference or an arithmetic error.
Frequently asked questions
What is the correct answer to this question?
663
Why is this the correct answer?
The sequence is an AP because consecutive terms differ by the constant amount d = 16 − 9 = 7. Thus a = 9 and n = 13. Use S_n = n/2[2a + (n − 1)d]: S_13 = 13/2[2(9) + 12(7)] = 13/2[18 + 84] = 13/2 × 102 = 13 × 51 = 663. Hence option C is correct. An equivalent check uses the last term: a_13 = 9 + 12 × 7 = 93, so S_13 = 13/2(9 + 93) = 663. The other options arise from an incorrect difference or an arithmetic error.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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