Question

15. Convert the following recursive formula to an explicit formula.a = 57: -3 . an-1

Answer 1

The recursive formula is

a = 57 ------- first term and d = -3 ------- common difference

`a_n=-3+a_(n-1)`

The explicit formula of the sequence is

`a_n=a+(n-1)d`

Where d is the constant difference between each 2 consecutive terms

∵ a is the first term

∴ a = 57

∵ d is the constant difference

∴ d = -3

→ Substitute them in the form above

`\therefore a_n=57+(n-1)*(-3)`

Let us simplify it

`\begin{gathered} \because a_n=57+n(-3)-1(-3) \\ \therefore a_n=57-3n+3 \\ \therefore a_n=(57+3)-3n \\ \therefore a_n=60-3n \end{gathered}`

Then the explicit formula is an = 60 - 3n