find a formula for the nth term of the arithmetic sequence. first term 1 common difference 4 ( a_{n}=?n+ )
find a formula for the nth term of the arithmetic sequence. first term 1 common difference 4 ( a_{n}=?n+ )
Answer
Explanation:
Step1: Recall the formula for the nth term of an arithmetic sequence
The formula for the (n)th term of an arithmetic sequence is (a_{n}=a_{1}+(n - 1)d), where (a_{1}) is the first term and (d) is the common difference.
Step2: Substitute the given values into the formula
Given (a_{1}=1) and (d = 4), we have (a_{n}=1+(n - 1)\times4).
Step3: Simplify the expression
[ \begin{align*} a_{n}&=1+4n-4\ a_{n}&=4n-3 \end{align*} ]
Answer:
(a_{n}=4n - 3), so the first box is (4) and the second box is (-3)