Question

In an ap the first term is 25 nth term is -17 and sum of first nth term is 60.find n and d the common difference

Answer 1

Sn=n/2(a+an)
60=n/2(25+(-17))
60=n/2(8)
60×2/8=n
n=15
now
an=a+(n-1)d
-17=25+(15-1)d
-17-25=14d
d=-42/14=-3
so,
n=15
d=-3

Answer 2

Answer:

$n=15$ and $d=3$

Step-by-step explanation:

It is given that in an AP, the first term is 25 and the nth term is -17.

Also, the sum of the first nth term is 60, then using

$S_{n}=\frac{n}{2}(a+a_{n})$

Substituting the given values, we get

$60=\frac{n}{2}(25+(-17))$

$60=\frac{n}{2}(8)$

$n=15$

Also, $a_{n}=a+(n-1)d$

Again substituting the given values, we get

$-17=25+(15-1)d$

$d=3$

Hence, the value of n and d are 15 and 3 respectively.