Question

if the first term of an AP is 22 , the common difference is -4 and the sum of n terms is 64 find n ? explain the double answer?

Answer 1

hey friend your answer is here......
a=22
d=-4
sn=64
n=?
sn=n/2(2a+(n-1)d)
64=n/2(2(22)+(n-1)-4)
$64 \times 2 = n{44 + (n - 1) - 4$
128=n(44-4n+4)

$128 = 44n - 4n {?}^{2} + {4n}$
128-44n+4nsquare-4n
$4n {?}^{2} - 48n + 128 = 0$
4(nsquare-12n+32)=0
$n {?}^{2} - 12n + 32 = 0$
n sq. -8n-4n+32=0
n(n-8)-4(n-8)=0
(n-4)(n-8)=0
n=4,8
hope it's help you friend....