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Find the sum of first 25 terms of an AP whose nth term is given by Tn equals 7 -3n?
The general expression for the nth term of an AP is : a + (n - 1)d, where a is the first term and d is the common difference.
Putting n = 1, then T1 = 7 - 3 = 4, which is the value of a.
Then 7 - 3n = 4 + (n - 1)d : 3 - 3n = (n - 1)d : -3(n - 1) = (n - 1) d : d = -3.
The formula for the sum of the AP to the nth term is : Sn = n/2[2a + (n - 1)d]
Therefore S25 = 25/2[2x4 + (25-1)x-3] = 25/2[8+(24 x -3)] = 25/2[8-72] = 25/2 x - 64 = -800
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