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Question
Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
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Solution
Here, we are given an A.P., whose nth term is given by the following expression,
`a_n = 5 -6n`
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 = 1in the given equation for nth term of A.P.
a = 5 - 6(1)
= 5 - 6
= -1
Now, the last term (l) or the nth term is given
`a_n = 5 - 6n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_n = (n/2) [(-1) + 5 - 6n]`
`= (n/2) [4 - 6n]`
`= (n/2) (2)[2 - 3n]`
= (n)(2 - 3n)
Therefore the sum of the n terms of the given A.P. is `(n)(2 - 3n)`
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