In an AP, the first term is (3), common difference is (5), and number of terms is (20). What is the sum of the first (20) terms?
Answer and explanation
Correct answer: (1010)
The governing concept is the sum of the first n terms of an arithmetic progression. Use S_n = n/2[2a + (n−1)d]. Here a = 3, d = 5, and n = 20. First calculate 2a = 6 and (n−1)d = 19 × 5 = 95. Their sum is 101, and multiplying by n/2 gives S_20 = 20/2 × 101 = 10 × 101 = 1010. Thus option A is correct. A quick check uses the last term: l = a + 19d = 98, so the average of the first and last terms is (3+98)/2 = 50.5; 20 × 50.5 also equals 1010. The other values result from arithmetic errors.
Frequently asked questions
What is the correct answer to this question?
(1010)
Why is this the correct answer?
The governing concept is the sum of the first n terms of an arithmetic progression. Use S_n = n/2[2a + (n−1)d]. Here a = 3, d = 5, and n = 20. First calculate 2a = 6 and (n−1)d = 19 × 5 = 95. Their sum is 101, and multiplying by n/2 gives S_20 = 20/2 × 101 = 10 × 101 = 1010. Thus option A is correct. A quick check uses the last term: l = a + 19d = 98, so the average of the first and last terms is (3+98)/2 = 50.5; 20 × 50.5 also equals 1010. The other values result from arithmetic errors.
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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