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Question
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
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Solution
For an A.P.
t8 = 37
`=>` a + 7d = 37 ...(i)
Also, t15 – t12 = 15
`=>` (a + 14d) – (a + 11d) = 15
`=>` a + 14d – a – 11d = 15
`=>` 3d = 15
`=>` d = 5
Substituting d = 5 in (i), we get
a + 7 × 5 = 37
`=>` a + 35 = 37
`=>` a = 2
∴ Required A.P. = a, a + d, a + 2d, a + 3d, .....
= 2, 7, 12, 17, .....
Sum of the first 20 terms of this A.P.
= `20/2 [2 xx 2 + 19 xx 5]`
= 10[4 + 95]
= 10 × 99
= 990
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