Let's make a table of differences
0 3 8 15 24
3 5 7 9
2 2 2
Constant second difference means a quadratic polynomial,
f(n)=an² + bn +c
f(1)=0, f(2)=3, f(3)=8
0 = a+b+c
3 = 4a + 2b + c
8 = 9a + 3b + c
Subtracting pairs
3 = 3a+b
5 = 5a + b
Subtracting,
2 = 2a
a = 1
b = 5 - 5a = 0
c = -a-b = -1
f(n)=n² -1
Duh, shoulda noticed that at the beginning.
f(17)=17²-1 = 288
a₁ =5
aₙ = aₙ₋₁ - 7
aₙ = a₁ + d(n-1)
aₙ = 5 - 7(n-1)
a₇ = 5 - 7(6) = -37
Answer: -37
Y = 3/2 + 5
since it’s perpendicular, flip the numerator and denominator of the slope and b=5 because it’s going through the y-axis at (0,5)
3,920,000,000,000 in scientific notation is 3.92x10^12
-3y = 2x - 7
when x = 0
-3y = -7
y = 7/3
y = 2 1/3(2 and 1/3)
when y = 0
2x - 7 = 0
2x = 7
x = 3.5
when x = 2
-3y = 2(2) - 7
-3y = -3
y = 1
when x = -1
-3y = 2(-1) - 7
-3y = -9
y = 3
Answer ( you can 3 of those below for your ordered pairs)
ordered pairs
(0, 7/3), (3.5, 0) (2, 1), (-1, 3)
