Intermediate Algebra
Consider the sequence {an}={4,1,−2,−5,⋯}\{a_{n}\}=\{4,1,-2,-5,\(\cdots\)\}. What is the value of a3a_3?
If the general term of a sequence is an=3n+2a_n = 3n + 2, what is the value of a10a_{10}?
Find the explicit formula for the arithmetic sequence {2,6,10,14,⋯}\{2, 6, 10, 14, \(\cdots\)\} in its simplest form.
Consider the sequence defined by an=(−1)n⋅n22n\(\displaystyle\) a_n = (-1)^n \(\cdot\) \(\frac{n^2}{2^n}\) for n≥1n \(\ge\) 1. Which classification best describes the behavior and properties of this sequence?
Find the explicit formula for the sequence {3,−5,7,−9,⋯}\{3, -5, 7, -9, \(\cdots\)\} by combining an arithmetic rule for the magnitude with an alternating sign factor.
