Find the sum of the first 20 terms of the AP (95, 89, 83, ...).
Answer and explanation
Correct answer: 760
The governing concept is the sum of a finite arithmetic progression. Here the first term is a = 95, the common difference is d = 89 − 95 = −6, and n = 20. First find the twentieth term: a20 = a + (n − 1)d = 95 + 19(−6) = 95 − 114 = −19. Now use S_n = n/2(a + l): S20 = 20/2(95 + (−19)) = 10 × 76 = 760. Hence option B is correct. The negative common difference only makes the sequence decrease; it does not make the sum negative. The other values result from an arithmetic or last-term error.
Frequently asked questions
What is the correct answer to this question?
760
Why is this the correct answer?
The governing concept is the sum of a finite arithmetic progression. Here the first term is a = 95, the common difference is d = 89 − 95 = −6, and n = 20. First find the twentieth term: a20 = a + (n − 1)d = 95 + 19(−6) = 95 − 114 = −19. Now use S_n = n/2(a + l): S20 = 20/2(95 + (−19)) = 10 × 76 = 760. Hence option B is correct. The negative common difference only makes the sequence decrease; it does not make the sum negative. The other values result from an arithmetic or last-term error.
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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