In an arithmetic series, if the sum of third and seventh terms is 8 and the sum of the sixth and the

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12 Aug 2022 Sequence & Series

In an arithmetic series, if the sum of third and seventh terms is 8 and the sum of the sixth and the tenth terms is 26, then what is the first term of the sequence?

OPtion

1) 2
2) 3
3) 0
4) 4
5) 1
6) -8
7) 5
8) -2
9) -5
10) None of these

Solution

nth term of an A.P a(n) = a1 + (n-1)d
Given, a3 + a7 = 8
(a1 + 2d) + (a1 + 6d) = 8
⇒ a1 + 4d = 4 ---(i)
And a6 + a10 = 26
(a1 + 5d) + (a1 + 9d) = 26
⇒ a1 + 7d = 13 ---(ii)
Solving Eqn. (i) & (ii), we get d=3, a1=-8
Correct Option 6)

Correct Option: 6 Best Solution (4)