What is the sum of the first 10 terms of the arithmetic progression (2, 5, 8, 11, …)?
Answer and explanation
Correct answer: 155
Direct answer: option D, 155. The first term is a = 2, the common difference is d = 5−2 = 3, and n = 10. For an arithmetic progression, Sₙ = n/2[2a + (n−1)d]. Therefore S₁₀ = 10/2[2(2) + 9(3)] = 5[4 + 27] = 5×31 = 155. Verify by finding the last term: a₁₀ = a + 9d = 2 + 9×3 = 29. The average of the first and last terms is (2 + 29)/2 = 15.5, and 10×15.5 = 155. Thus D is correct. A, B, and C do not satisfy the AP sum calculation. A common error is using 10d instead of (10−1)d when finding the tenth term, or counting eleven terms. Remember that ten terms contain nine equal steps after the first term.
Frequently asked questions
What is the correct answer to this question?
155
Why is this the correct answer?
Direct answer: option D, 155. The first term is a = 2, the common difference is d = 5−2 = 3, and n = 10. For an arithmetic progression, Sₙ = n/2[2a + (n−1)d]. Therefore S₁₀ = 10/2[2(2) + 9(3)] = 5[4 + 27] = 5×31 = 155. Verify by finding the last term: a₁₀ = a + 9d = 2 + 9×3 = 29. The average of the first and last terms is (2 + 29)/2 = 15.5, and 10×15.5 = 155. Thus D is correct. A, B, and C do not satisfy the AP sum calculation. A common error is using 10d instead of (10−1)d when finding the tenth term, or counting eleven terms. Remember that ten terms contain nine equal steps after the first term.
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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