Question

What are the recursive and explicit formulas for the following sequence?
Year 0: 10
Year 1: 30
Year 2: 90
Year 3: 270
Year 4: 810
Year 5: 2430

Answer 1

well the 1st term is 10 and then you multiply each term by 3

this is a geometric series a term can be found by using

\[a_{n} = a \times r^{n -1}\]

you know a the 1st term is 10 and the know the terms are multiplied by 3

so you can substituet these values to get the formula where n >= 1

the alternative formula is

\[a _{n + 1} = 3 \times a_{n} \]

again n > = 1

Answer 2

Thanks :D