Question

the algebric expression for the sum to n terms of an arthemetic sequence is n²+2n a)find its term and common difference b) prove that one more than the sum of first any number of terms of this arthemetic sequence is a perfect square​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

1

1

The algebra of an arithmetic sequence is n square +2n. What is the sum of this sequence?

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Nkumar

Answered October 13, 2018

Here tn=n^2+2n

Now t1=1^2 +2×1

t2=2^2 +2×2

t3=3^2+2×3

tn=n^2 +2n

Adding we have sn=(1^2+2^2+3^2+…..+n^2)+2(1+2+3+…+n)

sn={n(n+1)(2n+1)/6}+2×n(n+1)/2

=n(n+1)/2{2n+1/3+2}

=n(n+1)/2×{(2n+1+6)/3}

=n(n+1)(2n+7)/6