find the 66th term of the arithmetic sequence -10, 7, 24,...
find the 66th term of the arithmetic sequence -10, 7, 24,...
Answer
Explanation:
Step1: Find the common difference (d)
The common difference (d) of an arithmetic sequence is (d=a_{n + 1}-a_{n}). For (a_{1}=-10) and (a_{2}=7), (d = 7-(-10)=17).
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). Here (a_{1}=-10), (n = 66), and (d = 17). Substitute these values into the formula: [ \begin{align*} a_{66}&=-10+(66 - 1)\times17\ &=-10+65\times17\ &=-10 + 1105\ &=1095 \end{align*} ]
Answer:
(1095)