Question 444308: what is the nth term of: 3, 12, 27, 48, 75, 108...
What is the nth term of: 3, 6, 11, 18, 27,38...
What is the nth term of:4, 6.5, 9, 11.5, 14...
what is the nth term of: 20, 17, 14, 11, 8...
Please awnser fast. thanks
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
1.
take the differences between the numbers to get:
9, 15, 21, 27
take the second differences by taking the differences of the numbers above:
6, 6, 6
all the second differences are equal to six, which means the equation is quadratic: y=ax^2+bx+c
we can find the a, b, & c values by pluggin in the points (1,3), (2,12), & (3,27) and solving for a,b,& c by elimination:
1a+1b+1c=3
4a+2b+1c=12
9a+3b+1c=27
1a+1b+1c=3
3a+1b+0c=9
8a+2b+0c=24
1a+1b+1c=3
3a+1b+0c=9
2a+0b+0c=6
2a=6
a=3
3a+b=9
b=0
a+b+c=3
c=0
final equation of nth term is:  or
2.
The nth term is an equation to find any term using n the term you want to find.
so, the   for the sequence 2,3,4,5 is
3.
What is the nth term of:4, 6.5, 9, 11.5, 14...
the nth term is:
check:
4.
the nth term is:
check:
20 - (n-1)3....n=1...20
20 - (n-1)3....n=2...17
20 - (n-1)3....n=3...14
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