Question

Please Help! My question is in the picture.

Answer 1

First we need to determine the type of progression in the question.
That's geometric progression. Because the pattern from one sequence to the others are about multiplying.

Second, determine the ratio of the progression
r = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4

Third, determine the formula to know the recursive rule
a₂ = a × 1/4
a₂ = 1/4 × a
$a_{n} = \frac{1}{4} a_{(n-1)}$

Fourth, determine a₁. a₁ is the first term of the progression
a₁ = 2

Final answer:
Recursive rule
$a_{n} = \frac{1}{4} a_{(n-1)}$
a₁ = 2