In an AP, the sum of the first and last terms is 420, and the total sum is 7350. Find the number of terms.
Answer and explanation
Correct answer: 35
The governing formula for the sum of an arithmetic progression is S_n = n/2(a + l), where a is the first term and l is the last term. The question gives the combined value a + l = 420 and the total sum S_n = 7350, so substitute these directly: 7350 = n/2 × 420 = 210n. Dividing both sides by 210 gives n = 7350/210 = 35. Therefore, option C is correct. The common difference, first term separately, and last term separately are unnecessary here because their sum is already supplied. Options A, B, and D result from an incorrect division or substitution.
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
The governing formula for the sum of an arithmetic progression is S_n = n/2(a + l), where a is the first term and l is the last term. The question gives the combined value a + l = 420 and the total sum S_n = 7350, so substitute these directly: 7350 = n/2 × 420 = 210n. Dividing both sides by 210 gives n = 7350/210 = 35. Therefore, option C is correct. The common difference, first term separately, and last term separately are unnecessary here because their sum is already supplied. Options A, B, and D result from an incorrect division or substitution.
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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