Arithmetic sequence in senior one Given sequence {an} and {BN} satisfy bn=(a1+2*a2+3*a3+...+na4)/(1+2+3+...+n), If {an} is an arithmetic sequence, {BN} must be an arithmetic sequence, and vice versa Help, do right can add points | Math enthusiast | Mathematical art

Arithmetic sequence in senior one Given sequence {an} and {BN} satisfy bn=(a1+2a2+3a3+...+na4)/(1+2+3+...+n), If {an} is an arithmetic sequence, {BN} must be an arithmetic sequence, and vice versa Help, do right can add points

If the title is wrong, BN = (a1 + 2 * A2 + 3 * A3 +... + Na4) / (1 + 2 + 3 +... + n), it should be corrected to be BN = (a1 + 2 * A2 + 3 * A3 +... + Nan) / (1 + 2 + 3 +... + n). Prove: from the title, let an = a1 + (n-1) d, so Sn = (a1 + an) * n / 2 = n * a1 + (n-1) * n * D / 2 (arithmetic sequence summation formula 2), then BN =

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