Write the arithmetic sequence $-2,4,10,16, \ldots$ in the standard form:
\[
a_{n}=
\]

Answer

Expert–verified

Hide Steps

Answer

So, the final answer is $a_{n} = \boxed{6n - 8}$

Steps

Step 1 ：The standard form of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$, where $a_1$ is the first term and $d$ is the common difference.

Step 2 ：In this case, $a_1 = -2$ and $d = 4 - (-2) = 6$.

Step 3 ：We can substitute these values into the formula to get the standard form of the sequence.

Step 4 ：$a_{n} = -2 + (n-1)6 = -2 + 6n - 6 = 6n - 8$

Step 5 ：So, the final answer is $a_{n} = \boxed{6n - 8}$