An is an arithmetic sequence, CN = an ^ 2-A (n + 1) ^ 2 (n ∈ n *) (1) Judge whether the sequence cn is an arithmetic sequence (2) If a1 + a3 + +A25 = 130, A2 + A4 +... + A26 = 143-13k (k is a constant), try to write the general term formula of the sequence CN

An is an arithmetic sequence, CN = an ^ 2-A (n + 1) ^ 2 (n ∈ n *) (1) Judge whether the sequence cn is an arithmetic sequence (2) If a1 + a3 + +A25 = 130, A2 + A4 +... + A26 = 143-13k (k is a constant), try to write the general term formula of the sequence CN

Given the sequence {an}, where a1 = - 1 / 3, an = (an-1-1) / (an-1 + 3), let CN = 1 / (an + 1) (1) prove that {CN} is an arithmetic sequence; (2) find an

an=(an-1-1)/(an-1+3)
an+1=(an-1-1)/(an-1+3)+1=(2an-1+2)/(an-1+3)
1/(an+1)=(an-1+3)/(2an-1+2)=1/an-1+1/2
That is, CN = Cn-1 + 1 / 2
{CN} is an arithmetic sequence
cn=(n+2)/2
1/(an+1)=(n+2)/2
an=-n/(n+2)

Judge whether the sequence an = n ^ 2 + n is an arithmetic sequence, and explain the reason

a1=2,a2=6,a3=12
Obviously, A2-A3 is not equal to A2-A3
It's definitely not an arithmetic sequence
And a (n + 1) - A (n) = (n + 1) ^ 2 + (n + 1) - (n ^ 2 + n) = 2n + 2 is a variable, which means it is not an arithmetic sequence