Question

If the ratio of sums to n terms of two A.P.’ s is (5n + 7) :

(3n + 2), then the ratio of their 17^th terms is –

• A. 172 : 99
• B. 172 : 101
• C. 175 : 99
• D. 175 : 101

Answer 1

Answer: (B)

172 : 101

Answer 2

Let two A.P.’ s be a, a + d, a + 2d, a + 3d, .....and A, A + D, A + 2D, A + 3D,…..

According to the given condition,

$\frac{\frac{n}{2}\lbrack 2a + (n - 1)d\rbrack}{\frac{n}{2}\lbrack 2A + (n - 1)D\rbrack}$=$\frac{5n + 7}{3n + 2}$

Ž$\frac{a + \frac{n - 1}{2}d}{A + \frac{n - 1}{2}D}$= $\frac{5n + 7}{3n + 2}$

­­­­­­­­­­­­­­­­­­Putting $\frac{n - 1}{2}$ = 16 or n = 33, we get

$\frac{a + 16d}{A + 16D}$= $\frac{5(33) + 7}{3(33) + 2}$= $\frac{172}{101}$.