Question

The recursive formula of an arithmetic sequence is described below A1 = 19, an = an-1 + 6Write the explicit equation of this arithmetic sequence given the recursive formula

Answer 1

We have the sequence:

`\begin{gathered} a_1=19 \\ a_n=a_(n-1)+6 \end{gathered}`

We can derive the explicit equation by looking at the first terms of the sequence and deriving the pattern:

`\begin{gathered} a_1=19 \\ a_2=a_1+6=19+6 \\ a_2=a_2+6=(a_1+6)+6=a_1+2\cdot6=19+2\cdot6 \\ a_3=a_2+6=(a_1+2\cdot6)+6=a_1+3\cdot6=19+3\cdot6 \end{gathered}`

We then can generalize to:

`a_n=19+n\cdot6=19+6n`

Answer: the explicit formula is a_n=19+6n

`a_n=19+6n`