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

The correct option is B $172:101$

$\frac{Sn}{S{n}^1}=\frac{Sn+7}{3n+2}$

$\frac{=\frac{n}{2}[2a+(n-1\left)d\right]}{\frac{n}{2}[2a+(n-1\left)d\right]}$

$=\frac{a+(n-1)d/2}{a+(n-1)d/2}$

$\frac{n-1}{2}=16$

$n=33$

$\therefore \frac{Sn}{S{n}^1}=\frac{5\times 33+7}{3\times 33+2}$

$=\frac{172}{101}$