SOLUTION: Here are the first five terms of a sequence: 2,2,0,,-4,-10 An expression for the nth term of this sequence is 3n-n^2 Write down, in terms of n,an expression for the nth term o

Algebra ->  Equations -> SOLUTION: Here are the first five terms of a sequence: 2,2,0,,-4,-10 An expression for the nth term of this sequence is 3n-n^2 Write down, in terms of n,an expression for the nth term o      Log On


   

Question 924484: Here are the first five terms of a sequence:
2,2,0,,-4,-10
An expression for the nth term of this sequence is 3n-n^2
Write down, in terms of n,an expression for the nth term of a sequence whose first five terms are:
4,4,0,-8,-20
Please help :)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
4,4,0,-8,-20
all given terms are divisible by 2, and as you see all are 2 times the terms 2,2,0,-4,-10
then we can multiply %283n-n%5E2%29 by 2 and we get
2%283n-n%5E2%29-this is nth term
check if this formula for nth term gives you 4,4,0,-8,-20
2%283%2A1-1%5E2%29=2%283-1%29=2%2A2=4
2%283%2A2-2%5E2%29=2%286-4%29=2%2A2=4
2%283%2A3-3%5E2%29=2%289-9%29=2%2A0=0
2%283%2A4-4%5E2%29=2%2812-16%29=2%2A%28-4%29=-8
2%283%2A5-5%5E2%29=2%2815-25%29=2%2A%28-10%29=-20
but, I like higher degree first, and if you multiply 2%283n-n%5E2%29 by -1, you get
-2%28n%5E2-3n%29-this is nth term too
check:
-2%281%5E2-3%2A1%29=-2%281-3%29=-2%28-2%29=4
-2%282%5E2-3%2A2%29=-2%284-6%29=-2%28-2%29=4
-2%283%5E2-3%2A3%29=-2%289-9%29=-2%280%29=0
-2%284%5E2-3%2A4%29=-2%2816-12%29=-2%284%29=-8
-2%285%5E2-3%2A5%29=-2%2825-15%29=-2%2810%29=-20