Math Problem Solver

$$1.4,4.5,7.6,...$$The 8^th term in this arithmetic sequence is $\frac{231}{10}$.

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

Explicit Formula: $$a_n=\frac{31 n}{10} - \frac{17}{10}$$

Recursive Formula: $$a_n=a_{n-1} + \frac{31}{10}, \text{where } a_{1}=1.4$$

$$\begin{matrix}1.4&&4.5&&7.6\\[6pt]&+\frac{31}{10}&&+\frac{31}{10}\\[6pt]\end{matrix}$$

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 $d$: $$\begin{aligned} a_1&=\frac{7}{5} \\ d&=\frac{31}{10} \end{aligned}$$

The n^th term rule is:$$\begin{aligned} a_n&=a_1 + d (n - 1) \\ &=\frac{7}{5} + \frac{31}{10} (n - 1) \\ &=\frac{31 n}{10} - \frac{17}{10} \end{aligned}$$

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 $d$: $$\begin{aligned} d=\frac{31}{10} \end{aligned}$$

The n^th term rule is:$$\begin{aligned} a_n&=a_{n-1} + d \\ &=a_{n-1} + \frac{31}{10} \\ &=a_{n-1} + \frac{31}{10} \end{aligned}$$