If the ratio of the sum of the first n terms of two A.P is $(7 n + 1) : (4 n + 27)$ , find the ratio of their $9^{t h}$ terms.

Open in App

Solution

$\frac{S_{n}}{S_{n_{2}}} = \frac{7 n + 1}{4 n + 27}$

$\Rightarrow \frac{\frac{n}{2} [2 a + (n - 1) d_{1}]}{\frac{n}{2} [2 a + (n - 1) d_{2}]}$

replace $n$ by $(2 m - 1)$ ,

$\Rightarrow \frac{2 a_{1} + (2 m - 2) . d_{1}}{2 a_{2} + (2 m - 2) . d_{2}} = \frac{7 (2 m - 1) + 1}{4 (2 m - 1) + 27}$

$\Rightarrow \frac{2 [a_{1} + (m - 1) d_{1}]}{2 [a_{2} + (m - 1) d_{2}]} = \frac{14 m - 7 + 1}{8 m - 4 + 27}$

$\Rightarrow \frac{T_{m}}{T_{m}} = \frac{14 m - 6}{8 m + 23}$

$\Rightarrow \frac{T_{q}}{T_{q}} = \frac{14.9 - 6}{8.9 + 23} = \frac{126 - 6}{72 + 23}$

$\Rightarrow \frac{120}{95}$

$\frac{T_{q}}{T_{q}} = \frac{24}{19}$

Suggest Corrections

Similar questions

(7 n + 1) : (4 n + 27)

9^{t h}

If ratio of the sum of first n terms of two A.P is 7n+1:4n+27,then find the ratio of their 9th terms.

n

A . P s

(7 n + 1) : (4 n + 27)

10^{t h} t e r m

n

(7 n + 1) : (4 n + 27)

Join BYJU'S Learning Program