Question

What is the next term In the sequence $-8,-5,-2,$?

Answer 1

Step 1. Determine the difference between the first and second terms.

Take the difference between the first and second terms.

$\begin{array}{rcl}-5-\left(-8\right)& =& 3\\ -2-\left(-5\right)& =& 3\end{array}$

Thus, the common differences is $3$.

The recursive formula for the $n$th term is $a_n=a_1+\left(n-1\right)d$, where $d$ is the common difference and $a_1$ is the first term.

So, the next term in the given sequence is the fourth term. So, $n=4$ and $d=3$.

Thus, since the first of the given series is $-8$, $a_1=-8$.

Step 2. Determine the next term of the given series.

Substitute $n=4,d=3,\mathrm{and}{a}_1=-8$ into the recursive formula.

$\begin{array}{rcl}{a}_4& =& -8+\left(4-1\right)3\\ & \Rightarrow & a_4=-8+\left(3\right)3\\ & \Rightarrow & a_4=-8+9\\ & \Rightarrow & a_4=1\end{array}$

Hence, the next term in the given sequence is $1$.