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Question
Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.
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Solution
51 terms of an A.P whose `a_2 = 2` and `a_4 = 8`
Now
`a_2 = a + d`
2 = a + d .....(1)
Also
a_4 = a + 3d
8 = a+ 3d ....(2)
Substracting 1 from 2 we get
2d = 6
d = 3
Further substituting d = 3 in (1) we get
2 = a + 3
a = -1
Number of terms (n) = 51
First term for the given A.P. (a) = −1
So, using the formula we get,
`S_n = 51/2[2(-1) + (51 - 1)(3)]`
`= (51/2)[-2 +(50)(3)]`
`= (51/2)[-2 + 150]`
`= (51/2)[148]`
= 3774
Therefore the sum of first terms for given A.P. is 3774
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