Unit 7 test: Sequences and Series

A sequence is defined by $a_n = n^2 - 2n$. Find $a_7$.

Evaluate $\displaystyle\sum_{k=1}^{5} (3k - 1)$.

Which expression equals $3 + 6 + 9 + \cdots + 45$?

An arithmetic sequence has $a_1 = -4$ and $d = 7$. Find $a_{25}$.

Write an explicit formula for $a_n$ in the arithmetic sequence $20, 17, 14, 11, \dots$ Use $n$ for the position.

In the sequence $10, 16, 22, 28, \dots$, which term (what value of $n$) equals $250$?

Find the sum $4 + 11 + 18 + \cdots + 137$.

A geometric sequence has $a_1 = 2$ and $r = 3$. Find $a_7$.

Evaluate $\displaystyle\sum_{k=1}^{6} 4 \cdot 3^{k-1}$.

In a geometric sequence with a positive common ratio, $a_2 = 18$ and $a_4 = 2$. Find $a_1$.

Find the sum of the infinite series $45 - 15 + 5 - \dfrac{5}{3} + \cdots$.

Which infinite geometric series has a finite sum?

Write $0.\overline{36} = 0.363636\ldots$ as a fraction in lowest terms.

A sequence is defined by $a_1 = 3$ and $a_n = 2a_{n-1} - 1$. Find $a_4$.

A sequence follows the rule $a_n = 0.9\,a_{n-1} + 12$ with $a_1 = 20$. What value do the terms approach in the long run?