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

$a+12=–1$

$a=–13$

Now, General term = $a_n=a+(n–1)d=–13+(n–1)\times 2=2n–15$