Q. 34.3( 21 Votes )

Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.

Answer :

Since, nth term is given as (5 - 6n)

Put n = 1, we get a1 = - 1 = first term


Put n = 2, we get a2 = - 7 = second term


Now, d = a2 - a1 = - 7 - (-1) = - 6


Sum of first n terms = Sn= [2a + (n - 1)d]; where a is the first term


and d is the common difference.


= [ - 2 + (n - 1)(-6)]


= n[ - 1 - 3n + 3]


= n(2 - 3n)


sum of first 20 terms = S20


= [2(-1) + (20 - 1)(-6)]


= 10 × [ - 2 - 114]


= 10 × [ - 116]


= - 1160


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