What is the sum of the first 5 terms of the arithmetic progression (2,7,12,17, …)?
Answer and explanation
Correct answer: 60
The governing concept is the sum of the first n terms of an arithmetic progression. The first five terms are 2, 7, 12, 17, and 22, because the common difference is 5. Direct addition gives S₅ = 2 + 7 + 12 + 17 + 22 = 60, so option B is correct. The standard formula confirms this: Sₙ = n/2[2a₁ + (n − 1)d], hence S₅ = 5/2[2(2) + 4(5)] = 5/2(24) = 60. Option A, 55, omits 5 from the total; option C adds an extra 5; and option D is larger still because it does not represent the sum of exactly the first five terms.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
The governing concept is the sum of the first n terms of an arithmetic progression. The first five terms are 2, 7, 12, 17, and 22, because the common difference is 5. Direct addition gives S₅ = 2 + 7 + 12 + 17 + 22 = 60, so option B is correct. The standard formula confirms this: Sₙ = n/2[2a₁ + (n − 1)d], hence S₅ = 5/2[2(2) + 4(5)] = 5/2(24) = 60. Option A, 55, omits 5 from the total; option C adds an extra 5; and option D is larger still because it does not represent the sum of exactly the first five terms.
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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