Question

Determine the general term of an A.P. whose $7^{th}$ term is $-1$ and ${16}^{th}$ term $17$.

Answer 1

Let $a$ be the first term and $d$ be the common difference of the given A.P.
Let the A.P. be $a_1,a_2,a_3,...,a_n,...$

It is given that
$a_7=-1$ and $a_{16}=17$

$⟹a+(7-1)d=-1$ and $a+(16-1)d=17$

$⟹a+6d=-1$ ...(i)

and, $a+15d=17$ ...(ii)
Subtracting equation (i) from equation (ii), we get
$9d=18⟹d=2$
Putting $d=2$ in equation (i), we get
$a+12=-1⟹a=13$
Hence, General term $=a_n=a+(n-1)d=-13+(n-1)\times 2=2n-15$