What is the sum of the first 7 terms of the arithmetic progression (12, 10, 8, ...)?
Answer and explanation
Correct answer: 42
Use the AP sum formula S_n = n/2[2a + (n - 1)d]. The first term is a = 12, the common difference is d = 10 - 12 = -2, and the number of terms is n = 7. Hence S_7 = 7/2[24 + 6(-2)] = 7/2(24 - 12) = 7/2 × 12 = 42. Equivalently, the seventh term is 12 + 6(-2) = 0, so the average of the first and last terms is 6 and the sum is 7 × 6 = 42. Therefore option B is correct. The negative difference must not be replaced by +2.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
Use the AP sum formula S_n = n/2[2a + (n - 1)d]. The first term is a = 12, the common difference is d = 10 - 12 = -2, and the number of terms is n = 7. Hence S_7 = 7/2[24 + 6(-2)] = 7/2(24 - 12) = 7/2 × 12 = 42. Equivalently, the seventh term is 12 + 6(-2) = 0, so the average of the first and last terms is 6 and the sum is 7 × 6 = 42. Therefore option B is correct. The negative difference must not be replaced by +2.
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.
