find the 84th term of the arithmetic sequence -5, 15, 35,...
find the 84th term of the arithmetic sequence -5, 15, 35,...
Answer
Explanation:
Step1: Find the common difference
The common difference (d) of an arithmetic sequence is (d=a_{n + 1}-a_{n}). Here, (a_{1}=-5), (a_{2}=15), so (d = 15-(-5)=20).
Step2: Use the formula for the (n)th term of an arithmetic sequence
The formula for the (n)th term of an arithmetic sequence is (a_{n}=a_{1}+(n - 1)d). Substitute (a_{1}=-5), (d = 20), and (n = 84) into the formula: [ \begin{align*} a_{84}&=-5+(84 - 1)\times20\ &=-5+83\times20\ &=-5 + 1660\ &=1655 \end{align*} ]
Answer:
(1655)