What is the sum of the first 10 terms of the arithmetic progression (2, 5, 8, 11, …)?
Answer and explanation
Correct answer: 155
The governing concept is the sum of the first n terms of an arithmetic progression: Sₙ = n/2 [2a₁ + (n − 1)d]. In this sequence, a₁ = 2, d = 5 − 2 = 3, and n = 10. Thus S₁₀ = 10/2 [2(2) + 9(3)] = 5[4 + 27] = 5 × 31 = 155. The same result can be checked by finding the tenth term, a₁₀ = 2 + 9 × 3 = 29, and using S₁₀ = 10/2(2 + 29) = 5 × 31 = 155. Options A, B, and C result from using an incorrect difference, term count, or arithmetic simplification. Therefore, option D is correct.
Frequently asked questions
What is the correct answer to this question?
155
Why is this the correct answer?
The governing concept is the sum of the first n terms of an arithmetic progression: Sₙ = n/2 [2a₁ + (n − 1)d]. In this sequence, a₁ = 2, d = 5 − 2 = 3, and n = 10. Thus S₁₀ = 10/2 [2(2) + 9(3)] = 5[4 + 27] = 5 × 31 = 155. The same result can be checked by finding the tenth term, a₁₀ = 2 + 9 × 3 = 29, and using S₁₀ = 10/2(2 + 29) = 5 × 31 = 155. Options A, B, and C result from using an incorrect difference, term count, or arithmetic simplification. Therefore, option D is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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