How many terms of AP : 54,51,48,.... must be taken so that their sum is 513 ? Explain the double answer.
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Answer:
18 or 19
Step-by-step explanation:
a=54
d=-3
Sn=513
since Sn=n/2*[2a+(n-1)d]
513=n/2[108+(n-1)-3]
1026=n[108-3n+3]
1026=108n-3n*2+3n
3n*2-111n+1026=0
dividing throughout by 3 we get,
n*2-37n+342=0
n*2-18n-19n+342=0
n(n-18)-19(n-18)=0
n-18 or n-19
n=18 or n=19
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