Question

in an ap 16 14 12 the sum of how many terms are 60 why we get double answer explain?​

Answer 1

Answer:

Given:- a=16 , a2=14 , Sn=60

{we have to find n(number of terms)}

we know that,

d=a2-a=14-16=(-2)

(.•. Sn=n/2{2a+(n-1)d}

60=n/2{2×16+(n-1)(-2)}

120=n(32-2n+2)

120=n(34-2n)

120=34n-2n²

2n²-34n+120=0

n²-17n+60=0

(.:. it is a quadratic equation n should have two values)

i.e., n²-5n-12n+60=0

n(n-5)-12(n-5)=0

(n-12) (n-5)=0

n=12 or n=5. :°_°:Ans