If the 5th term of an arithmetic sequence is 18 and the 15th term is 58, what is the sum of the first 25 terms?
- 1250
- 1300
- 1350
- None of these
Explanation
For an A.P., nth term = a + (n-1)d, where a = first term, d = common difference
Given:
a5 = a + 4d = 18
a15 = a + 14d = 58
Subtract: 10d = 40 → d = 4
Put d=4 in a + 4d = 18 → a + 16 = 18 → a = 2
Sum of first n terms = n/2 [2a + (n-1)d]
S25 = 25/2 [2×2 + 24×4]
= 25/2 [4 + 96]
= 25/2 × 100 = 25 × 50 = 1250
Last verified on 13-06-2026
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