Question

Given the recursive formula for a geometric sequence find the common ratio, the first five terms, and the explicit formula an= an_1 .2 a1 =2

Answer 1

$Geometric\ sequence:\\\\a_n=a_{n-1}\ * 2\\a_1=2$

common ratio =  $\frac{a_n}{a_{n-1}}=2$

a₁ =  2  = 2¹
a₂ = a₁ * 2 =  4 = 2¹ * 2 = 2²
a₃ = a₂ * 2 =  8  =  2² * 2 = 2³
a₄ = a₃ * 3 = 16
a₅ =  a₄ * 2 = 32

So the non recursive direct formula  for
$a_n = 2^n$