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The sum of a certain number of terms of an AP series –8, –6, –4, …… is 52. The number of terms is
  • a)
    12
  • b)
    13
  • c)
    11
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Answers

a = -8, 
d =2, 
Sn= 52, 
we know that, 
Sn=n/2[2a+(n-1)d] 
52=n/2[-16+2n-2] 
n(n-9)=52 
n^2-9n-52=0 
(n-13)(n+4)=0 
n=13 since n=-4 is impossible.

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The sum of a certain number of terms of an AP series –8, –6, –4, …… is 52. The number of terms isa)12b)13c)11d)none of theseCorrect answer is option 'B'. Can you explain this answer?
Formula is n/2(2a+(n-1)d)
so n/2(2(-8)+(n-1)2)=n/2(-16+2n-2)
=n/2(-18+2n)=52
-18n+2n^2=104
n^2-9n-52=0
n^2-13n+4n-52=0
n(n-13)+4(n-13)=0
(n-13)(n+4)=0
n=13. n=-4
Here we consider only positive values so n=13
Hence it is proved

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a = -8,d =2,Sn= 52,we know that,Sn=n/2[2a+(n-1)d]52=n/2[-16+2n-2]n(n-9)=52n^2-9n-52=0(n-13)(n+4)=0n=13 since n=-4 is impossible.