What is the sum of the first 11 terms of an arithmetic progression if the 3rd term is -1 and the 8th term is 19?
What is the sum of the first 11 terms of an arithmetic progression if the 3rd term is -1 and the 8th term is 19?
1). 204
2). 121
3). 225
4). 104
1 answers
Let the first term of AP be a and common difference be d
From the problem’s statement
3rd term = a + (3 - 1)d = a + 2d = -1 ----(i)
8th term = a + (8 - 1)d = a + 7d = 19 ----(ii)
Now (ii) - (i)
⇒ 5d = 20
⇒ d = 4,
put this in (i)
a = - 1 - 8 = - 9
Now the sum of first 11 term = (11/2)(2a + (11 - 1)d)
⇒ Sum = (11/2)(-18 + 10 × 4) = 121
∴ sum of first 11 terms of AP is 121
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