Q. 223.7( 6 Votes )

In an AP, the first term is – 4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

Answer :

Here, first term = a = - 4

Let the Common difference = d


Last term = l = 29


Sum of all terms = Sn = 150


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 = [ - 4 + 29] = 150


25n = 300


n = 12


there are 12 terms in the AP.


Thus 29 is the 12th term of the AP.


29 = a + (12 - 1)d


29 = - 4 + 11d


29 + 4 = 11d


11d = 33


d = 3


Common difference = d =3


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