Find a formula for the nth term of the sequence

Question

geometric
a1=4, ak+1 =1/2 ak

my answer
an=4(1/2)^n-1

Answer 1

Your answer is correct.

a₁ = 4

aₖ₊₁ = aₖ / 2

a₁₊₁ = a₂ = a₁ / 2 = 4 / 2 = 2

a₂₊₁ = a₃ = a₂ / 2 = 2 / 2 = 1

a₃₊₁ = a₄ = a₃ / 2 = 1 / 2

etc.

r = a₂ / a₁ = 2 / 4 = 1 / 2

r = a₃ / a₂ = 1 / 2

r = a₄ / a₃ = ( 1 / 2 ) / 1 = 1 / 2

In your geometric sequence, a = a₁ = 4 , r = 1 / 2

The n-th term of a geometric sequence:

aₙ = a ∙ r ⁿ ⁻ ¹

aₙ = 4 ( 1 / 2 )ⁿ ⁻ ¹

Answer 2

Also:

4=2^2

(1/2)^(n-1) =2^(-(n-1))=2^(-n+1)

an=4(1/2)^(n-1)=2^2*2^(-n+1)=2^2*2^(-n)*2^1=
2^2*2^1*2^(-n)=2^(2+1)*2^(-n)=2^3*2^(-n)=2^(3-n)