Calculus 2: Sequences

What is the sixth term of the arithmetic sequence if the first term is 3 and the common difference is 2?

Write a formula to find the 20th term of the arithmetic sequence where the first term is 3 and the common difference is 2.

Calculate the sum of the first 40 terms of the arithmetic sequence with a first term of 3 and a common difference of 2.

Determine the fifth term of the geometric sequence where the first term is 5 and the common ratio is 3.

Calculate the sum of the first 10 terms of the geometric sequence where the first term is 5 and the common ratio is 3.

Write a rule for the arithmetic sequence given two terms: The third term is 7, and the fifth term is 13.

Write a rule for the geometric sequence given two terms: The second term is 6, and the fifth term is 162.

Using the summation notation $\Sigma$, calculate the sum of the arithmetic series from $k=1$ to $k=10$ with the arithmetic rule $a_k = 3k + 2$.

Find out what a sequence does in the limit of $N\to\infty$ for the sequence A sub N equals N.

Determine if the sequence $A_n = \frac{N}{N+1}$ is convergent or divergent as $N \to \infty$.

Find the missing term in the sequence 2, 5, 10, _, 26 by identifying the pattern.

Find the missing term in the Fibonacci-like sequence 1, 2, 3, 5, 8, _, 21 where each term is the sum of the previous two terms.

Given the sequence $a_n = (-1)^n (n - 2)$, find the first five terms of the sequence.

Given the sequence $b_n = \frac{3n}{n+4}$, find the first five terms of the sequence and reduce if necessary.

Given the recursive sequence $c_0 = 2$ and $c_{n+1} = c_n + 4$, find the first five terms of the sequence.

Determine if the sequence $a_n = \frac{n-1}{n!}$ converges or diverges as $n \to \infty$.

Determine if the sequence $a_n = 1 + \frac{(-1)^n}{n^2}$ converges or diverges as $n \to \infty$.

Determine if the sequence $a_n = \sqrt[3]{\frac{n}{n+1}}$ converges or diverges as $n \to \infty$.