Math Problem Solver

$$1,9,17,...$$The next term in this arithmetic sequence is $a_{4}=25$.

The nth term in this sequence is given by the formula:

Explicit Formula: $$a_n=8 n - 7$$

Recursive Formula: $$a_n=a_{n-1} + 8, \text{where } a_{1}=1$$

$$\begin{matrix}1&&9&&17\\[6pt]&+8&&+8\\[6pt]\end{matrix}$$

Explicit Formula

The formula for an arithmetic sequence where $a_1$ is the 1^st term, $d$ is the common difference, and $n$ is the term number is $$a_n=a_1 + d (n - 1)$$

Find $a_1$ and $d$: $$\begin{aligned} a_1&=1 \\ d&=8 \end{aligned}$$

The n^th term rule is:$$\begin{aligned} a_n&=a_1 + d (n - 1) \\ &=1 + 8 (n - 1) \\ &=8 n - 7 \end{aligned}$$

Recursive Formula

The formula for an arithmetic sequence where $a_{n-1}$ is the (n-1)^th term, $d$ is the common difference, and $n>1$ is $$a_n=a_{n-1} + d$$

Find $d$: $$\begin{aligned} d=8 \end{aligned}$$

The n^th term rule is:$$\begin{aligned} a_n&=a_{n-1} + d \\ &=a_{n-1} + 8 \\ &=a_{n-1} + 8 \end{aligned}$$