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:)
Substitute n for the value you need, but you have to do them in order:
So = 2
S1 = 5
S2 = - S2-1 + 2S2-2
= - 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
S2=-1
To interpret the value of "n" in the given equation, we need to understand its meaning in the context of the sequence that is being defined. In this case, the equation Sn = -Sn-1 + nSn-2, n >= 2 is a recurrence relation that defines each term of the sequence S0, S1, S2, S3, and so on.
The value of "n" in the equation represents the index of the term in the sequence. For example, S0 represents the term at index 0, S1 represents the term at index 1, S2 represents the term at index 2, and so on.
Therefore, "n" is not equivalent to S1, S0, or 2. Instead, "n" represents the position of the term in the sequence. In order to find a specific term, such as S3, we substitute the value of "n" as 3 in the given equation and calculate it using the defined recurrence relation.
To solve for S3, we can use the equation Sn = -Sn-1 + nSn-2, where n = 3:
S3 = -S2 + 3S1
To find S2, substitute the value of n as 2:
S2 = -S1 + 2S0
And to find S1 and S0, you can use the given values S0 = 2 and S1 = 5.
By following the steps mentioned above, you can compute the value of S3 and any other term in the sequence defined by the recurrence relation.