find the nth term in this number sequence:
1,7,13,19
MathBot Answer:
$$1,7,13,19,...$$This infinite sequence is an arithmetic sequence. The nth term rule for the sequence is $a_n=6 n - 5$, where $n>0$. The recursive formula is $a_n=a_{n-1} + 6$, where $n>1$ and $a_{1}=1$.
$$\begin{matrix}1&&7&&13&&19\\[6pt]&+6&&+6&&+6\\[6pt]\end{matrix}$$
Explicit Formula
The formula for an arithmetic sequence where $a_1$ is the 1st term, $d$ is the common difference, and $n$ is the term number is $$a_n=a_1 + d (n - 1)$$
Find $a_1$ and $d$: $$\begin{aligned} a_1&=1 \\ d&=6 \end{aligned}$$
The nth term rule is:$$\begin{aligned} a_n&=a_1 + d (n - 1) \\ &=1 + 6 (n - 1) \\ &=6 n - 5 \end{aligned}$$
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 $d$: $$\begin{aligned} d=6 \end{aligned}$$
The nth term rule is:$$\begin{aligned} a_n&=a_{n-1} + d \\ &=a_{n-1} + 6 \\ &=a_{n-1} + 6 \end{aligned}$$
asked 9 days ago
active 9 days ago