Question

In an A.P given an=4,d=2,Sn=-14,find n and a?​

Answer 1

an=a+(n-1)d

4=a+(n-1)d

4=a+2n-2

a=4-2n+2

a=2-2n

Sn= n/2(2a+(n-1)d)

-14=n/2(2a+(n-1)2)

-14=n/2(2a+(2n-2))

put value of a

-14=n/2(2(2-2n)+(2n-2))

-14=n/2(3(2-2n))

-14=3n(2-2n)/2

-14=3×2(1-n)/2

-14=3(1-n)/2

-14×2=3(1-n)

-28/3=(1-n)

-28/3-1=-n

-28-3/3= -n

-31/3= -n

n=31/3

a=2-2n

a=2-2×31/3

a=2-62/3

a= -60/3

a= -20