Question

A geometric sequence is defined recursively by
a(n) = 4a(n-1). The 10th term of the sequence is a(10) = 3.5. What is a(13)?

Answer 1

4 is the ratio right?

Answer 2

A{n} = 4A{n-1}
= 4(4A{n-2})
= 4(4(4A{n-3}))
= 4^3 A{n-3}

= 4^r A{n-r} ; when n-r = 0 when r=n

= 4^n A{0}

A{10} = 3.5 = 4^10 A{0}
3.5/(4^10) = A{0}

A{n} = 4^n (3.5)/4^10 ... maybe :)

Answer 3

A{10} = 4^10 (3.5)/4^10 = 3.5 ; lol

A{13} = 4^13 (3.5)/4^10 = 224