Question

If $7$ times the $7th$ term of an $A.P$. is equal to $11$ times the $11th$ term, then find the value of $\frac{a}{d}$.

Answer 1

As we know that, $n^{th}$ term in an A.P. is given as

$a_n=a+(n-1)d$

Here $a$ and $d$ are the first term and common difference respectively.

Now,

$a_7=a+(7-1)d=a+6d$

$a_{11}=a+(11-1)d=a+10d$

According to the question

$7a_7=11a_{11}$

$\Rightarrow 7(a+6d)=11(a+10d)$

$\Rightarrow 7a+42d=11a+110d$

$\Rightarrow 11a-7a=42d-110d$

$\Rightarrow 4a=-68d$

$\Rightarrow \frac{a}{d}=\frac{-68}{4}=-17$