Question

To write the explicit rule, we need some information about the following series:

3, 6, 12, 24, 48, ...

In Blank 1: a1 =
In Blank 2: r =

Answer 1

see explanation

Explanation:

Note the common ratio r between consecutive terms of the sequence

r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2

The explicit rule for a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 3 and r = 2, thus

`a_(n)` = 3
`(2)^(n-1)` ← explicit rule