Question

find the value of n and a if an=4 , d=2,sn=-14​

Answer 1

an =a+(n-1)d=4

or, a+(n-1)2=4

or, a+2n-2=4

or, a+2n=4+2

or, a+2n=6

or, a=6-2n

Sn = n/2[2a+(n-1)d]=-14

or, n/2[2a+(n-1)2]=-14

or, an+n(n-1)=-14

or, (6-2n)n+n²-n=-14

or, 6n-2n²+n²-n=-14

or, -n²+5n=-14

or, n²-5n=14

or, n²-5n-14=0

or, n²-7n+2n-14=0

or, n(n-7)+2(n-7)=0

or, (n-7)(n+2)=0

either, n-7=0

or, n=7

or, n+2=0

or, n=-2

∵, n can not be negative ;

∴, n=7

∴, a=6-(2×7)

=6-14

=-8

∴, n=7 and a=-8 Ans.