Question

If for an AP S8= 16 and S16= 8 find the first negative term

Answer 1

a+7d=16, a+15d=8

8d=-8, d=-1 ,a=23

For first negative no

a+(n-1)d<0

23-(n-1)<0

n>24

So first negative will be when n=25.

A(25)=23+(25–1)(-1)=-1

Hope This Helps :)

Answer 2

Answer:

-1

Step-by-step explanation:

Formula of nth term of AP = $a_n=a+(n-1)d$

Substitute n=8

$a_8=a+(8-1)d$

$a_8=a+7d$

$16=a+7d$ ---A

Substitute n =16

$a_{16}=a+(16-1)d$

$a_{16}=a+15d$

$8=a+15d$  --B

Subtract B from A

$16-8=a+7d-a-15d$

$d=-1$

Substitute value of d in A

$16=a+7(-1)$

$23=a$

For first negative no

a+(n-1)d<0

23-(n-1)<0

n>24

So first negative will be when n=25.

Substitute n = 25 in Formula given above

$a_{25}=23+(25-1)(-1)$

$a_{25}=-1$

Hence the first negative term is -1