What is the sum of the first 8 terms of the arithmetic progression (10, 17, 24, 31, ...)?

276

Direct answer: option B, 276. In an arithmetic progression, each term changes by the same common difference. The first term is a = 10, the common difference is d = 17 − 10 = 7, and there are n = 8 terms. The sum formula is Sₙ = n/2[2a + (n − 1)d]. Substitution gives S₈ = 8/2[2(10) + (8 − 1)7] = 4[20 + 49] = 4 × 69 = 276. We can check by finding the last term: a₈ = a + (8 − 1)d = 10 + 7 × 7 = 59. The average of the first and last terms is (10 + 59)/2 = 34.5, and 8 × 34.5 = 276. Therefore B is correct. A, 268, is 8 less than the correct result; C, 284, and D, 292, also do not satisfy the sum formula or the average check. The common mistake is using 8d instead of 7d for the eighth term: eight terms contain only seven equal jumps from the first term. Remember: the nth term uses n − 1 steps, and the sum formula then multiplies the average by n.

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.