Q. 245.0( 5 Votes )

The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find the common difference and the number of terms.

Answer :

Here, first term = a = 5

Let the Common difference = d


Last term = l = 45


Sum of all terms = Sn = 400


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 = [5 + 45] = 400


50n = 800


n = 16


there are 16 terms in the AP.


Thus 45 is the 16th term of the AP.


45 = a + (16 - 1)d


45 = 5 + 15d


40 = 15d


15d = 40


d = 8/3


Common difference = d = 8/3


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