Question

The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is

(a) $\frac{179}{321}$

(b) $\frac{178}{321}$

(c) $\frac{175}{321}$

(d) $\frac{176}{321}$

Answer 1

In the given problem, the ratio of the sum of n terms of two A.P’s is given by the expression,

We need to find the ratio of their 18^th terms.

Here we use the following formula for the sum of n terms of an A.P.,

Where; a = first term for the given A.P.

d = common difference of the given A.P.

n = number of terms

So,

Where, a and d are the first term and the common difference of the first A.P.

Similarly,

Where, a’ and d^’ are the first term and the common difference of the first A.P.

So,

Equating (1) and (2), we get,

Now, to find the ratio of the n^th term, we replace n by. We get,

As we know,

Therefore, for the 18^th terms, we get,

Hence

Hence no option is correct.