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Question
Find the sum of all 11 terms of an A.P. whose 6th term is 30.
Solution
Given, 6th term of A.P. = 30
or, a6 = 30
or, a + (6 – 1)d = 30
or, a + 5d = 30 ...(i)
Since, Sum of n terms of A.P. is Sn = `n/2[2a + (n - 1)d]`
∴ S11 = `11/2[2a + (11 - 1)d]`
= `11/2[2d + 10d]`
= `(11 xx 2)/2 [a + 5d]`
= 11 × 30 ...[From equation (i)]
= 330
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