In an AP, the sum of the first and last terms is 260, and the total sum is 4160. Find the number of terms.
Answer and explanation
Correct answer: 32
The governing formula for the sum of n terms of an arithmetic progression is S_n = n/2 × (first term + last term), or S_n = n/2(a + l). Here, a + l = 260 and S_n = 4160. Substituting these values gives 4160 = n/2 × 260 = 130n. Therefore, n = 4160/130 = 32. Hence option D is correct. The common difference and the individual first or last term are unnecessary because their sum is already provided. Options A, B, and C do not produce the given total when multiplied by 130.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The governing formula for the sum of n terms of an arithmetic progression is S_n = n/2 × (first term + last term), or S_n = n/2(a + l). Here, a + l = 260 and S_n = 4160. Substituting these values gives 4160 = n/2 × 260 = 130n. Therefore, n = 4160/130 = 32. Hence option D is correct. The common difference and the individual first or last term are unnecessary because their sum is already provided. Options A, B, and C do not produce the given total when multiplied by 130.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
