Question

Write an explicit rule and a recursive rule for each sequence

Answer 1

`a_(n)` = 1.3n - 4.7

Explanation:

There is a common difference d between consecutive terms

d = - 2.1 - (- 3.4) = - 0.8 - (- 2.1) = 0.5 - (- 0.8) = 1.8 - 0.5 = 1.3

This indicates the sequence is arithmetic with nth term ( explicit rule )

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3.4 and d = 1.3 , then

`a_(n)` = - 3.4 + 1.3(n - 1) = - 3.4 + 1.3n - 1.3 = 1.3n - 4.7

A recursive rule allows a term in the sequence to be found by adding d to the previous term, that is

`a_(n)` =
`a_(n-1)` + 1.3 : a₁ = - 3.4