Question

So = 2
S1 = 5
Sn = - Sn - 1 + nSn - 2, n >_ 2

How do I interpret the value of n? Is this number equivalent to S1, S0, or 2? I have tried each option; finding S3 is difficult because I don't know what value to multiply Sn-2 with, when solving for S2. Your assistance would be very helpful:)

Answer 1

Substitute n for the value you need, but you have to do them in order:
So = 2
S1 = 5

S₂ = - S_2-1 + 2S_2-2
= - S₁ + 2S₀
= -5 + 2*2
= -1

S2=1

S3=-S2+2*s1
=-(-1) + 2*5
=11

and so on.

Unfortunately, you will have to calculate all the terms in sequence for a recurrence relation UNLESS you solve for the sequence in terms of the initial terms.

I believe you are at the point where you need to be able to evaluate in sequence and understand the notations.





Sn = - Sn - 1 + nSn - 2, n >_ 2

Answer 2

S2=-1