Question

The third term of an A.P. is $18$, and the seventh term is $30$; find the sum of $17$ terms.

Answer 1

Let the first term of an AP be $a$ and common difference be $d$

The third term of an AP is $a+2d$, given that it is equal to $18$

$\Rightarrow a+2d=18$

The seventh term of an AP is $a+6d$, given that it is equal to $30$

$\Rightarrow a+6d=30$

By subtracting first equation from second equation , we get $4d=12$

$\Rightarrow d=3$

By substituting the value of $d$ it in first equation, we get $a=12$

Therefore sum of first $17$ terms in AP is $\frac{17}{2}(2\times 12+(17-1)\times 3)=\frac{17}{2}\times 72=612$