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Question
Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`
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Solution
Here, we are given an A.P. whose nth term is given by the following expression `a_n = An +B`.
We need to find the sum of first 20 terms.
So, here we can find the sum of the n terms of the given A.P., using the formula,
`S_n = (n/2) (a + l)`
Where a = the first term
l = the last term
So, for the given A.P,
The first term (a) will be calculated using n = 1 in the given equation for the nth term of A.P.
a = A(1) + B
= A + B
Now, the last term (l) or the nth term is given
`I = a_n = An + B`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_20 = (20/2)[(A + B) + A(20) + B]`
= 10[21A + 2B]
= 210A + 20B
Therefore the sum of the first 20 terms of the given A.P is `S_20 = 210A + 20B`
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