Question

Find an equation for the nth term of the arithmetic sequence. -1, 2, 5, 8, ...

Answer 1

Answer:

The expression for the n-th term is $a_n = -4+3n.$

Step-by-step explanation:

We know that the n-th term of an arithmetic progression is given by $a_n= a+nd$. So we need to find the coefficients $a$ and $d$. In order to do this, we substitute the values $n=1$ and $n=2$ in the expression for $a_n$:

$a_1 = a+d = -1,$

$a_2 = a+2d = 2.$

Now, notice that we have two linear equations with two unknowns, which it is not difficult to solve. Thus, the solution is $d=3$ and $a=-4$.

Hence, the expression for the n-th term is $a_n = -4+3n.$

We can check that the expression is correct substituting the values $n=3$ which gives $a_3 = 5$ and $n=4$ which gives $a_4 = 8$, as it is given in the statement of the problem.

Answer 2

-1 + 3(n-1)
hope this helps you