If an AP has a = −20, d = 9, and n = 30, what is the value of S₃₀?
Answer and explanation
Correct answer: 3315
The governing concept is the sum formula for the first n terms of an arithmetic progression: S_n = n/2[2a + (n − 1)d]. Substitute a = −20, d = 9 and n = 30. Then S30 = 30/2[2(−20) + 29(9)] = 15[−40 + 261] = 15 × 221 = 3315. Equivalently, the last term is l = −20 + 29 × 9 = 241, so S30 = 30/2(−20 + 241) = 15 × 221 = 3315. Therefore option D is correct. The negative first term must be retained; dropping its sign produces a nearby but incorrect result.
Frequently asked questions
What is the correct answer to this question?
3315
Why is this the correct answer?
The governing concept is the sum formula for the first n terms of an arithmetic progression: S_n = n/2[2a + (n − 1)d]. Substitute a = −20, d = 9 and n = 30. Then S30 = 30/2[2(−20) + 29(9)] = 15[−40 + 261] = 15 × 221 = 3315. Equivalently, the last term is l = −20 + 29 × 9 = 241, so S30 = 30/2(−20 + 241) = 15 × 221 = 3315. Therefore option D is correct. The negative first term must be retained; dropping its sign produces a nearby but incorrect result.
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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