write an equation for the nth term of the arithmetic sequence 4, 7, 10, 13, ...
write an equation for the nth term of the arithmetic sequence 4, 7, 10, 13, ...
Answer
Explanation:
Step1: Identify the first term and common difference
The first term (a_1 = 4). The common difference (d=7 - 4=3).
Step2: Use the formula for the nth term of an arithmetic sequence
The formula for the nth term of an arithmetic sequence is (a_n=a_1+(n - 1)d). Substitute (a_1 = 4) and (d = 3) into the formula: (a_n=4+(n - 1)\times3).
Step3: Simplify the expression
[ \begin{align*} a_n&=4+3n-3\ a_n&=3n + 1 \end{align*} ]
Answer:
(a_n = 3n+1)