Question

Find the explicit formula for the given sequence.
4, 24, 144,864, ....

Answer 1

`a_(n)` = 4
`(6)^(n-1)`

Explanation:

Note the terms in the sequence have a common ratio, that is

r = 24÷ 4 = 144÷ 24 = 864 ÷ 144 = 6

This indicates the sequence is geometric with n th term

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

Here a = 4 and r = 6, thus

`a_(n)` = 4
`(6)^(n-1)` ← explicit formula

Answer 2

x * 6

Explanation:

4 * 6 = 24

24 * 6 = 144

144 * 6 = 864