In an AP, d = 7, n = 16 and S₁₆ = 1176. Find the first term a.
Answer and explanation
Correct answer: 21
The governing concept is the sum formula for the first n terms of an AP: Sₙ = n/2 [2a + (n - 1)d]. Substitute n = 16, d = 7 and S₁₆ = 1176: 1176 = 16/2 [2a + 15(7)] = 8(2a + 105). Dividing by 8 gives 147 = 2a + 105, so 2a = 42 and a = 21. Therefore option A is correct. The other numerical choices result from an arithmetic error, using the wrong factor for n - 1, or failing to divide the total sum by the correct multiplier. The value of d is positive, so the progression increases from its first term.
Frequently asked questions
What is the correct answer to this question?
21
Why is this the correct answer?
The governing concept is the sum formula for the first n terms of an AP: Sₙ = n/2 [2a + (n - 1)d]. Substitute n = 16, d = 7 and S₁₆ = 1176: 1176 = 16/2 [2a + 15(7)] = 8(2a + 105). Dividing by 8 gives 147 = 2a + 105, so 2a = 42 and a = 21. Therefore option A is correct. The other numerical choices result from an arithmetic error, using the wrong factor for n - 1, or failing to divide the total sum by the correct multiplier. The value of d is positive, so the progression increases from its first term.
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.
