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Question
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Solution
Here, we are given an A.P. whose nth term is given by the following expression, `a_n = 2 - 3n`. We need to find the sum of first 25 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 = 2 - 3(1)
= 2 - 3
= -1
Now, the last term (l) or the nth term is given
`l = a_n = 2 - 3n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_25 = (25/2)[(-1)+2 -3(25)]`
`= (25/2)[1 - 75]`
`= (25/2)(-74)`
`= (25)(-37)`
= -925
Therefore, the sum of the 25 terms of the given A.P. is `S_25 = -925`
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