If an AP has a = -35, d = 12, and n = 28, what is the value of S₍₂₈₎?
Answer and explanation
Correct answer: 3556
For an arithmetic progression, the sum of the first n terms is Sₙ = n/2[2a + (n − 1)d]. Here a = −35, d = 12, and n = 28. Substitution gives S₂₈ = 28/2[2(−35) + 27(12)] = 14[−70 + 324] = 14 × 254 = 3556. The negative first term must be retained while calculating 2a; changing its sign would produce an incorrect result. Therefore option C is correct. The other values are plausible arithmetic-error distractors, usually caused by mishandling the negative sign, using 26d or 28d, or making a final multiplication error.
Frequently asked questions
What is the correct answer to this question?
3556
Why is this the correct answer?
For an arithmetic progression, the sum of the first n terms is Sₙ = n/2[2a + (n − 1)d]. Here a = −35, d = 12, and n = 28. Substitution gives S₂₈ = 28/2[2(−35) + 27(12)] = 14[−70 + 324] = 14 × 254 = 3556. The negative first term must be retained while calculating 2a; changing its sign would produce an incorrect result. Therefore option C is correct. The other values are plausible arithmetic-error distractors, usually caused by mishandling the negative sign, using 26d or 28d, or making a final multiplication 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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