Question

If the sum of n terms of on A.P. is n2, then its nth term is ​

Answer 1

aₙ=(2n-1)

Given--->

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sum of first n terms =n²

sₙ=n²

Solution--->

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sₙ=n²

putting n= 1 , s₁=1²=1

s₁ is sum of first term which is equal to first term

a₁=s₁ =1

now putting n=2 in sₙ

s₂ =2²=4

s₂ is sum of first two terms so

a₁+a₂=s₂=4

1 + a₂=4

a₂=4-1=3

now a₁=1,d=a₂-a₁=3-1=2,n=n,aₙ=?

we have formula of nth term of AP

aₙ=a+(n-1)d

=1+(n-1)2

=1+2n-2

=(2n-1)

Additional information--->

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1) sₙ =n/2{2a+(n-1)d}

where a =first term ,d =common difference ,n =no of terms

2) sₙ=n/2(a+l)

l =last term

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