How many terms of the AP 63, 60,57,54, ... must be taken so that their
sum is 693? Explain the double answer.
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Answer:
a= 63
d=60-63= -3
Sn= 693
Sn=n/2(2a+(n-1)d)
693= n/2(2×63 + (n-1)-3)
693×2= n(126-3n+3)
1386= n(129-3n)
1386=129n-3n²
3n²-129n+1386=0
n²-43n+462=0
n²-22n-21n+462=0
n(n-22)-21(n-22)= 0
(n-21)(n-22)=0
n-21=0 , n-22=0
n=21, n=22
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