Question

In an A.P. the third term is four times the first term, and the sixth term is $17$; find the series.

Answer 1

Given that in an AP , the third term is four times the first term

Let the first term be $a$ and the common difference be $d$

$\Rightarrow a+2d=4\times a$

$\Rightarrow 2d=3a$

Given that the sixth term is $17$

$\Rightarrow a+5d=17$

$\Rightarrow \frac{2d}{3}+5d=17$

$\Rightarrow d=\frac{3}{17}\times 17=3$

Therefore we get $d=3$ and $a=\frac{2d}{3}=2$

So the series is $2,5,8,11,14,17,...........$