Question

Help me please with math

Answer 1

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