In an AP, the sum of the first and last terms is 340, and the total sum is 5780. Find the number of terms.
Answer and explanation
Correct answer: 34
For an arithmetic progression with n terms, the sum is Sₙ = n/2(a + l), where a is the first term and l is the last term. The problem directly gives a + l = 340 and Sₙ = 5780. Substituting these values, 5780 = n/2 × 340 = 170n. Dividing both sides by 170 gives n = 5780/170 = 34. Therefore option B is correct. There is no need to determine the common difference, the individual end terms, or any intermediate term. Options 32, 36, and 38 arise from using an incorrect factor of 2 or making an arithmetic error while dividing.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
For an arithmetic progression with n terms, the sum is Sₙ = n/2(a + l), where a is the first term and l is the last term. The problem directly gives a + l = 340 and Sₙ = 5780. Substituting these values, 5780 = n/2 × 340 = 170n. Dividing both sides by 170 gives n = 5780/170 = 34. Therefore option B is correct. There is no need to determine the common difference, the individual end terms, or any intermediate term. Options 32, 36, and 38 arise from using an incorrect factor of 2 or making an arithmetic error while dividing.
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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