Which term of the AP – 2, - 7, - 12, … will be - 77? Find the sum of this AP upto the term - 77.


Given, AP – 2, - 7, - 12, …


Let the nth term of an AP is - 77.


Then, first term, a = - 2


common difference, d = - 7 – (2) = - 7 + 2 = - 5.


Let nth term of an AP is - 77


an = a + (n - 1)d


- 77 = - 2 + (n - 1) (- 5)


- 75 = (n - 1) (- 5)


15 = n - 1


n = 16


so 16th term of AP is - 77


S16 is the sum of AP upto the term - 77 .i.e. 16th term


As, Sn = (a + an) [ as last term is given]


= (- 2 - 77)


= 8 (- 79) = - 632


So 16th term is - 77 and sum upto 16th term is - 632


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