Find the numbers ofvtrems the ap 63,60 57......so that their sum is 693 explain the double answer
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Let n be number of terms.
let a be first term
let l be last term
let sum of terms be Sn
let d be common difference
Sn=n(a+l)/2
l=a+(n-1)d
=>
2*693=n(2a+(n-1)d)
d=-3
=>
n(126-3n+3)=1386
Or
-3n^2+129n-1386=0
By quadratic formula we get
n=21 or n=22
Please note that a quadratic equation has 2 roots
let a be first term
let l be last term
let sum of terms be Sn
let d be common difference
Sn=n(a+l)/2
l=a+(n-1)d
=>
2*693=n(2a+(n-1)d)
d=-3
=>
n(126-3n+3)=1386
Or
-3n^2+129n-1386=0
By quadratic formula we get
n=21 or n=22
Please note that a quadratic equation has 2 roots
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