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if an a.p consists of 31 terms and it’s 16 th term is p, then sum of all terms of the given a.p is ?

if an a.p consists of 31 terms and it’s 16th term is p,
then sum of all terms of the given a.p is ?

Grade:10

1 Answers

Sayam
49 Points
5 years ago
Let first term of AP is a and common difference d
As 16th term of AP is p.
So, p=a+15d ….…...(i)
Sum of n terms=n/2[2a+(n-1)d]
so sum of 31 terms = 31/2[2a+30d]
=31[a+15d]
=31[p] ….…....from eq(i)
=31 p
hope this clears your doubt

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