The sum of the first 24 terms of the arithmetic progression x, x+5, x+10, ... is 1788. What is x?
Answer and explanation
Correct answer: 17
Use the sum formula Sₙ = n/2[2a + (n−1)d] for an arithmetic progression. In this sequence, the first term is a = x, the common difference is d = 5, and n = 24. Therefore 1788 = 24/2[2x + 23(5)] = 12(2x + 115). Dividing by 12 gives 149 = 2x + 115. Subtracting 115 gives 2x = 34, so x = 17. Thus option C is correct. Option 15 would produce a sum of 1740, while 16 and 18 would produce different sums; they arise from mishandling the 23d term or dividing incorrectly.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
Use the sum formula Sₙ = n/2[2a + (n−1)d] for an arithmetic progression. In this sequence, the first term is a = x, the common difference is d = 5, and n = 24. Therefore 1788 = 24/2[2x + 23(5)] = 12(2x + 115). Dividing by 12 gives 149 = 2x + 115. Subtracting 115 gives 2x = 34, so x = 17. Thus option C is correct. Option 15 would produce a sum of 1740, while 16 and 18 would produce different sums; they arise from mishandling the 23d term or dividing incorrectly.
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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