Question

If the sums of n terms of two arithmetic progressions are in the ratio 3n+5:5n-7, then their n^th terms are in the ratio
(a) 3n-15:n-1
(b) 3n+15:n+1
(c) 5n+13:n+1
(d) 5n-13:n-1

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 n^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, we get,

Hence the correct option is (b).