Question

is the term of an ap is 22 and the common difference is -4 and the sum of n terms is 64 find n​

Answer 1

Given d=-4

Sn =64 and a=22

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

64=n/2[2(22)+(n-1)-4]

128=n[44-4n+4]

128=-4n sq +48n

4n sq - 48n +128 =0

4n sq - 16n - 32n + 128=0

4n(n-4)-32(n-4)=0

(n-4)(4n-32)=0

n=4 and n =8

n= 4(or)8