what is the general term of minus5, minus2, 1
MathBot Answer:
$$-5,-2,1,...$$This infinite sequence is an arithmetic sequence. The nth term rule for the sequence is $a_n=3 n - 8$, where $n>0$. The recursive formula is $a_n=a_{n-1} + 3$, where $n>1$ and $a_{1}=-5$.
$$\begin{matrix}-5&&-2&&1\\[6pt]&+3&&+3\\[6pt]\end{matrix}$$
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 $d$: $$\begin{aligned} a_1&=-5 \\ d&=3 \end{aligned}$$
The nth term rule is:$$\begin{aligned} a_n&=a_1 + d (n - 1) \\ &=-5 + 3 (n - 1) \\ &=3 n - 8 \end{aligned}$$
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 $d$: $$\begin{aligned} d=3 \end{aligned}$$
The nth term rule is:$$\begin{aligned} a_n&=a_{n-1} + d \\ &=a_{n-1} + 3 \\ &=a_{n-1} + 3 \end{aligned}$$