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.

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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