It is known that sequence {an} is an arithmetic sequence, CN = an ^ 2-A (n + 1) ^ 2 (n belongs to n *) If a1 + a3 +... + A9 = 30, A2 + A4 +... + A10 = 35-5k (k is a constant), try to write the general term formula of the sequence {CN};

It is known that sequence {an} is an arithmetic sequence, CN = an ^ 2-A (n + 1) ^ 2 (n belongs to n *) If a1 + a3 +... + A9 = 30, A2 + A4 +... + A10 = 35-5k (k is a constant), try to write the general term formula of the sequence {CN};

Since the sequence {an} is an arithmetic sequence, then: an = a1 + (n-1) d
From the sum formula of the first n terms of the arithmetic sequence: S = n * a1 + n (n-1) d / 2
A1 + a3 +... + A9 = 5 * a1 + 5 * 4 * 2D / 2 = 30 (tolerance d = 2D)
A2 + A4 +... + A10 = 5 * A2 + 5 * 4 * 2D / 2 = 35-5k (tolerance d = 2D)
The solution is: D = 1-k, A1 = 2 + 4K
Cn=an^2-a(n+1)^2=(an-a(n+1))*(an+a(n+1))
=(-d)*(a1+(n-1)*d+a1+n*d)
=(-d)*(2a1+2nd-d)
= -d*2a1-(2n-1)d^2
= -2(1-k)*(2+4k)-(2n-1)*(1-k)^2
=(k-1)(9k+3+2n-2nk)