Question

Find the sum of first $17$ terms of an AP whose $4^{th}$ and $9^{th}$ terms are $15$ and $30$ respectively.

Answer 1

Let a and d be the first term and the common difference of the given AP respectively. Then,

$a_4=15\Rightarrow a+3d=15$ ...(1)

$a_9=30\Rightarrow a+8d=30$ ...(2)

On subtracting (2) from (1), we get

$5d=15\Rightarrow d=3$

Putting d=3 in (1), we get

$a=15-3\times 3=6$

Now, Required sum=$S_{17}=\frac{17}{2}[2\times 6+(17-1)\times 3]$

$\Rightarrow S_{17}=\frac{17}{2}\left[60\right]=510$