SOLUTION: for the sequence, describe the pattern, write the next term, and write a rule for the nth term. ( the x's are 1,2,3,4,5) 1) 3, 1, -1, -3, ..... 2) -3, -24, -81, -192, .....

Algebra ->  Expressions-with-variables -> SOLUTION: for the sequence, describe the pattern, write the next term, and write a rule for the nth term. ( the x's are 1,2,3,4,5) 1) 3, 1, -1, -3, ..... 2) -3, -24, -81, -192, .....      Log On


   

Question 176909: for the sequence, describe the pattern, write the next term, and write a rule for the nth term. ( the x's are 1,2,3,4,5)
1) 3, 1, -1, -3, .....
2) -3, -24, -81, -192, .....
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1) Looks like you subtract 2 from the previous term to get the next term.
Or start at 3 and subtract 2 at each successive term.
a%5B1%5D=3-2%281-1%29=3
a%5B2%5D=3-2%282-1%29=3-2=1
a%5B3%5D=3-2%283-1%29=3-4=-1
a%5B4%5D=3-2%284-1%29=3-6=-3
a%5B5%5D=3-2%285-1%29=3-8=-5
-5 would be the next term.
a%5Bn%5D=3-2%28n-1%29=3-2n%2B2=5-2n
.
.
.
2) Looks like each term is a product of the cubes with (-3)
a%5B1%5D=%28-3%29%2A%281%29%5E3=-3
a%5B2%5D=%28-3%29%2A%282%29%5E3=-24
a%5B3%5D=%28-3%29%2A%283%29%5E3=-81
a%5B4%5D=%28-3%29%2A%284%29%5E3=-192
a%5B5%5D=%28-3%29%2A%285%29%5E3=-375
a%5Bn%5D=%28-3%29%2An%5E3
-375 would be the next term.
a%5Bn%5D=%28-3%29%2An%5E3