Question 1017219: Find the next two terms in the sequence –5, 8, –13, 20, –29, …. Write a formula for the nth term. Identify the formula as explicit or recursive
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the formula will be:
An = -1 * An-1 + (-1)^n * (2n-1)
it's a recursive formula that depends on the value of the term in the sequence immediately before it.
set A1 = -5
when n = 1, A1 = -5
when n = 2, An = -1 * An-1 + (-1)^n * (2n-1) becomes:
-1 * -5 + (-1)^2 * (2*2-1) which becomes:
-5 + 1 * (4 - 1) which becomes:
5 + 1 * 3) which becomes:
5 + 3 which is equal to 8.
when n = 3, An = -1 * An-1 + (-1)^n * (2n-1) becomes:
-1 * 8 + (-)^3 * (2*3-1) which becomes:
-8 - 1 * (6 - 1) which becomes:
-8 - 1 * 5 which becomes:
-8 - 5 which is equal to -13.
when n = 4, An = -1 * An-1 + (-1)^n * (2n-1) becomes:
-1 * -13 + (-1)^4 * (2*4-1) which becomes:
13 + 1 * (8-1) which becomes:
13 + 1 * 7 which becomes:
13 + 7 = 20
when n = 5, An = -1 * An-1 + (-1)^n * (2n-1) becomes:
-1 * 20 + (-1)^5 * (2*5-1) which becomes:
-20 - 1 * (10-1) which becomes:
-20 - 1 * 9 which becomes:
-20 - 9 = -29
the formula looks good.
your solution is that the formula is:
An = -1 * An-1 + (-1)^n * (2n-1)
An is the value of the nth term in the sequence starting at n = 2.
An-1 is the value of the term immediately preceding the nth term.
n is the number of the term with the first term in the sequence starting at 1.
the value of A1 is set to -5.
|
|
|
