Q. 44 A4.2( 13 Votes )

The sum of 17 terms of two series in A.P. are in the ratio (3n + 8) : (7n + 15). Find the ratio of their 12th terms.

Answer :

There are two AP with different first term and common difference.


For the First AP


Let first term be a


Common difference = d


Sum of n terms =


and nth term = an = a + (n – 1)d


For the second AP


Let first term be A


Common difference = D


Sum of n terms =


and nth term = An = A + (n – 1)D


It is given that





…(i)


Now, we need to find ratio of their 12th term






Hence,


n – 1 = 11 × 2


n = 22 + 1


n = 23


Putting n = 23 in eq. (i), we get






Hence the ratio of 12th term of 1st AP and 12th term if 2nd AP is 7:16


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