SOLUTION: How do you write equation for this sequence 16, 28, 42, 56

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Question 1167274: How do you write equation for this sequence 16, 28, 42, 56
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

On your TI calculator,
Press STAT
Press ENTER
Under L1, store 1, 2, 3, 4
Under  L2, store 16, 28, 42, 56
Press STAT
Press the right arrow key to highlight CALC
Press 6 for 6:CubicReg
See this screen:

     CubicReg
Xlist:L1
Xlist:L2
Store RegEQ:
Calculate

Press down arrow key 4 times to highlight Calculate

Press ENTER

See this screen:
    
    CubicReg
y=ax3+bx2+cx+d
a=-0.333333333
b=3
c=5.3333333333
d=8
R2=1

Interpret -0.333333333 as -1/3
interpret  5.333333333 as 5 1/3 and then as 16/3

So the equation is this, using n for x:

a%5Bn%5D=expr%28-1%2F3%29n%5E3%2B3n%5E2%2Bexpr%2816%2F3%29n%2B8

Checking:

for n=1

a%5B1%5D=expr%28-1%2F3%29%281%29%5E3%2B3%281%29%5E2%2Bexpr%2816%2F3%29%281%29%2B8
a%5B1%5D=expr%28-1%2F3%29%281%29%2B3%281%29%2Bexpr%2816%2F3%29%2B8
a%5B1%5D=-1%2F3%2B3%2B16%2F3%2B8
a%5B1%5D=-1%2F3%2B9%2F3%2B16%2F3%2B24%2F3
a%5B1%5D=48%2F3
a%5B1%5D=16

for n=2

a%5B2%5D=expr%28-1%2F3%29%282%29%5E3%2B3%282%29%5E2%2Bexpr%2816%2F3%29%282%29%2B8
a%5B2%5D=expr%28-1%2F3%29%288%29%2B3%284%29%2Bexpr%2832%2F3%29%2B8
a%5B2%5D=-8%2F3%2B12%2B32%2F3%2B8
a%5B2%5D=-8%2F3%2B36%2F3%2B32%2F3%2B24%2F3
a%5B2%5D=84%2F3
a%5B2%5D=28

for n=3

a%5B3%5D=expr%28-1%2F3%29%283%29%5E3%2B3%283%29%5E2%2Bexpr%2816%2F3%29%283%29%2B8
a%5B3%5D=expr%28-1%2F3%29%2827%29%2B3%289%29%2Bexpr%2848%2F3%29%2B8
a%5B3%5D=-27%2F3%2B27%2B48%2F3%2B8
a%5B3%5D=-27%2F3%2B81%2F3%2B48%2F3%2B24%2F3
a%5B3%5D=126%2F3
a%5B3%5D=42

for n=4

a%5B4%5D=expr%28-1%2F3%29%284%29%5E3%2B3%284%29%5E2%2Bexpr%2816%2F3%29%284%29%2B8
a%5B4%5D=expr%28-1%2F3%29%2864%29%2B3%2816%29%2Bexpr%2864%2F3%29%2B8
a%5B4%5D=-64%2F3%2B48%2B64%2F3%2B8
a%5B4%5D=-64%2F3%2B144%2F3%2B64%2F3%2B24%2F3
a%5B4%5D=168%2F3
a%5B4%5D=56

For more terms, calculate as above:

16,28,42,56,68,76,78,72,56,28,-14,-72,-148,...

Edwin