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
Answer:
(x, y) = (2, 1)
Step-by-step explanation:
Adding the two equations gives ...
2y = 2
y = 1 . . . . . divide by 2
Subtracting the second equation from the first gives ...
0 = 6x -12
0 = x -2 . . . . divide by 6
2 = x
The solution is (x, y) = (2, 1).
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The attached graph verifies this solution.
$25.99x
Step-by-step explanation:
As, for 1 song = $0.99 + $25
So, 1 song = $25.99
So, x song = $25.99 multiplied by x
Which is = $25.99x
So answer = $25.99x