Q. 253.9( 15 Votes )

In an AP, the first term is 22, nth term is – 11 and sum of first n terms is 66. Find n and hence find the common difference.

Answer :

Here, first term = a = 22

Let the Common difference = d


nth term = an = - 11


Sum of first n terms = Sn = 66


Let there be n terms in the AP.


Now, Sum of n terms of this arithmetic series is given by:


Sn = [2a + (n - 1)d]


= [a + a + (n - 1)d]


= [a + an]


Therefore sum of n terms of this arithmetic series is given by:


Sn = [22 + (-11)] = 66


11n = 132


n = 12


there are 12 terms in the AP.


Thus nth is the 12th term of the AP.


- 11 = a + (12 - 1)d


- 11 = 22 + 11d


- 11 - 22 = 11d


11d = - 33


d = - 3


Common difference = d = - 3


n = 12, d = - 3


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