How To Solve A Function F(x) Has These Properties The Domain Of F Is The Set Of Natural Numbers F (1)1 F (x plus 1)f(x) plus 3x(x plus 1) plus 1 A. Determine F (2) F(3) F (4) F (5) F(6) THANKS!!!!!!?

Answer 1

The function (sequence generator) f(x) with x∈ℕ has been defined as a recursive function (sequence), with the initial value defined for some x, ie starting form some some natural number (in this case 1), the value of the function (sequence) is given (in this case f(1) = 1), and each successive value of the function (sequence) is defined in terms of the current value f(x+1) = f{x} + g(x) where g(x) is a function with g(x) = 3x(x + 1).

f(x + 1) = f(x) + 3x(x + 1)

f(1) = 1

→ f(2) = f(1 + 1) = f(1) + (3×1)(1 + 1) = 1 + 3×2 = 1 + 6 = 7

→ f(3) = f(2 + 1) = f(2) + (3×2)(2 + 1) = 7 + 6×3 = 7 + 18 = 25

I'll let you evaluate the rest.

Hint:

f(4) = f(3 + 1) = f(3) + (3×3)(3 + 1)

f(5) = f(4 + 1) = f(4) + ...

f(6) = f(5 + 1) = f(5) + ...