Proving the sum formula of the first n terms of arithmetic sequence by induction It's urgent,

Proving the sum formula of the first n terms of arithmetic sequence by induction It's urgent,

Sn = n * a1 + n (n-1) d / 2 when n = 1, S1 = A1. Suppose that SK = k * a1 + K (k-1) d / 2 equation holds when n = K + 1, then s (K + 1) = SK + a (K + 1) = sk + A1 + k * d = k * a1 + K (k-1) d / 2 + A1 + k * d = (K + 1) * a1 + ((K & sup2; - K) d + 2K * d) / 2 = (K + 1) * a1 + (K & sup2; + k) d / 2 = (K + 1) * a1 + (K + 1) / (K + 1)

What is the general term formula of Fibonacci sequence?
What can I get from this formula?

This sequence was put forward by Fibonacci in Italy in the 13th century, so it is called Fibonacci sequence. The sequence is determined by the following recurrence relation: F0 = 0, F1 = 1, FN + 2 = FN + FN + 1 (n > = 0). Its general formula is FN = 1 / radical 5 {[(1 + radical 5) / 2] n-th power - [(1-radical 5) / 2] n-th power} (n belongs to positive integer) complement

Given that the sum of the first n terms of a sequence is (n ∧ 2) + 1, the general term is 2N-1, but A1 = S1 = 2 can be obtained from the sum of the first n terms, and A1 = 1 can be obtained from the general term formula. What makes A1 different?
How much is A1

Because the sum of the first n terms of the sequence determines that it is not a complete arithmetic sequence
You can see that all the formulas of the sum of the first n terms of the arithmetic sequence are an ^ 2 + BN (a, B are constants, a and B are not equal to 0 at the same time), that is to say, there is no constant term in the formula of the sum of the first n terms of the arithmetic sequence, but the formula of the sum of the first n terms of your question has a constant term 1, so it is not the sum of the first n terms of the arithmetic sequence