Answer:
Correct answer is: f(1) = - 21 , f(n) = - 3 · f(n -1)
Step-by-step explanation:
Given geometric sequence: -21, 63, -189, 567,.........................
Formula for n-th term or a₍ₙ₎ = f(n) = a₁ · q ⁽ⁿ⁻¹⁾ where a₁ is first term and q is quotient (ratio). Formula for (n-1) th term or a₍ₙ₋₁₎ = f(n-1) = a₁ · q ⁽ⁿ⁻²⁾
In this case a₁ = -21 and q = -3
a₍₁₎ = f(1) = -21 · (-3)⁽¹⁻¹⁾ = -21 · (-3)⁰ = -21
f(n) = q¹ · f(n - 1) = q¹ · a₁ q ⁽ⁿ⁻²⁾ = a₁ · q ⁽ⁿ⁻¹⁾ = f(n)
In this case q = -3
f(n) = -3 · f(n -1)
God with you!!!
