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How many terms of the A.P -15, -11, -7, ....... are needed to make the sum 744 ?

Posted by Mitra Suresh 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Mohammad Amaan 6 years, 5 months ago

a=-15, d=-11+15=4 , Sn=744 Sn=n/2{2a+(n-1)d} , n/2{-30+(n-1)4}=744 , n/2(-30+4n-4)=744 , n(-34+4n)=1488 , 4n^2-34n-1488=0 , 2n^2-17n-744=0 , 2n^2-48n+31n-744=0 , 2n(n-24)+31(n-24)=0 , (n-24)(2n+31)=0. , n=24 or n=-31/2(which is not possible). Hence,n=24

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Mohammad Amaan 6 years, 5 months ago

24 terms.

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