If the ratio of the sum to terms of two A.P.'s is , then the ratio of their terms is

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Solution

Q.
If the ratio of the sum to $n$ terms of two A.P.'s is $(5 n + 3) : (3 n + 4)$ , then the ratio of their $4^{t h}$ terms is

1 $\frac{16}{23}$

2 $\frac{23}{16}$

3 $\frac{38}{25}$

4 $\frac{25}{38}$

Ans.
(3)

Given $\frac{\frac{n}{2} [2 a_{1} + (n - 1) d_{1}]}{\frac{n}{2} [2 a_{2} + (n - 1) d_{2}]} = \frac{5 n + 3}{3 n + 4}$

For $n = 7, \frac{a_{1} + 3 d_{1}}{a_{2} + 3 d_{2}} = \frac{38}{25}$

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