If an arithmetic progression has a = 3, d = 7, and n = 20, what is the sum of the first 20 terms?
Answer and explanation
Correct answer: 1390
For an arithmetic progression, the sum of the first n terms is Sₙ = n/2[2a + (n − 1)d]. Substituting a = 3, d = 7, and n = 20 gives S₂₀ = 20/2[2(3) + 19(7)] = 10[6 + 133] = 10 × 139 = 1390. Therefore option D is correct. As a check, the twentieth term is a₂₀ = 3 + 19 × 7 = 136, and the sum is 20/2 × (first term + last term) = 10 × (3 + 136) = 1390. The other options arise from mishandling 19d or the factor n/2.
Frequently asked questions
What is the correct answer to this question?
1390
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]. Substituting a = 3, d = 7, and n = 20 gives S₂₀ = 20/2[2(3) + 19(7)] = 10[6 + 133] = 10 × 139 = 1390. Therefore option D is correct. As a check, the twentieth term is a₂₀ = 3 + 19 × 7 = 136, and the sum is 20/2 × (first term + last term) = 10 × (3 + 136) = 1390. The other options arise from mishandling 19d or the factor n/2.
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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