Given that the first n terms and Sn of sequence {an} are quadratic functions of N, and its first three terms A1 = - 2, A2 = 2. A3 = 6, then A100 =? | Math enthusiast | Mathematical art

Given that the first n terms and Sn of sequence {an} are quadratic functions of N, and its first three terms A1 = - 2, A2 = 2. A3 = 6, then A100 =?

Let Sn = an ^ 2 + BN + C, then:
S1=a1=A+B+C=-2
S2=a1+a2=4A+2B+C=0
S3=a1+a2+a3=9A+3B+C=6
The solution is a = 2, B = - 4, C = 0
That is, Sn = 2n ^ 2-4n
a100=S100-S99=2×100^2－4×100－2×99^2＋4×99＝394

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