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Question
The sum of 41 terms of an A.P. with middle term 40 is ______.
Options
820
1640
2460
None of these
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Solution
The sum of 41 terms of an A.P. with middle term 40 is 1640.
Explanation:
Since middle term = 40
`\implies` T21 = 40
`\implies` a + 20d = 40 ...(1)
We know that,
`S_n = n/2[2a + (n - 1)d]`
∴ `S_41 = 41/2[2a + 40d]`
= `41/2 xx 2[a + 20d]`
= 41 × 40 ...[Using (1)]
= 1640
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