The sum of 11 terms of two A.P.'s are in the ratio (5n + 4) : (9n + 6), find the ratio of their 18th terms.

Question

Philoid · Accepted 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 n^th term = a_n = a + (n – 1)d

For the second AP

Let first term be A

Common difference = D

Sum of n terms =

and n^th term = A_n = A + (n – 1)D

It is given that

…(i)

Now, we need to find ratio of their 18^th term

Hence,

n – 1 = 17 × 2

⇒ n = 34 + 1

⇒ n = 35

Putting n = 35 in eq. (i), we get

Hence the ratio of 18^th term of 1^st AP and 18^th term if 2^nd AP is 179:321