Question

in an A.P firstterm is 22,the common difference is-4 and sum of nterms is 64 .find n?​

Answer 1

a = 22, d = -4

Sn = 64

n/2[a+an] = 64

n/2[a+a+(n-1)d] = 64

n/2[ 2×22 + (n-1)(-4)] = 64

n/2[ 44-4n+4] = 64

n[ 22-2n+2] =64

24n-2n² -64 = 0

2n² -24n+64 =0

n²-12n+32 =0

n²-8n-4n+32 =0

n(n-8)-4(n-8) =0

(n-8)(n-4) =0

so, n =8, n=4

value of n are 8,4 which gives sum 64