Q. 214.1( 10 Votes )

In an AP, the first term is 2, the last term is 29 and the sum of all the terms is 155. Find the common difference.

Answer :

Here, first term = a = 2

Let the Common difference = d


Last term = l = 29


Sum of all terms = Sn = 155


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 + l]


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


Sn = [2 + 29] = 155


31n = 310


n = 10


there are 10 terms in the AP.


Thus 29 be the 10th term of the AP.


29 = a + (10 - 1)d


29 = 2 + 9d


27 = 9d


d = 3


common difference = d =3


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