Sequences Practice

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What does it mean for a sequence to converge?

Back

A sequence converges if its terms approach a specific value as the number of terms increases.

Front

What does it mean for a sequence to diverge?

Back

A sequence diverges if its terms do not approach any specific value as the number of terms increases.

Front

What is the limit of the sequence \( \frac{1}{n^2} \) as \( n \) approaches infinity?

Back

The limit is 0.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term in the sequence is multiplied to get the next term.

Front

Given the geometric sequence 2, 6, 18, ..., what is the common ratio?

Back

The common ratio is 3.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula \( a_n = a_1 \cdot r^{(n-1)} \), where \( a_1 \) is the first term and \( r \) is the common ratio.

Front

What is the formula for the sum of the first n terms of a geometric series?

Back

The formula is \( S_n = a_1 \frac{1 - r^n}{1 - r} \) for \( r \neq 1 \).

Front

What is the fifth term of the geometric sequence 5, 15, 45,...?

Back

The fifth term is 405.

Front

What does \( b_c = 7 \left( \frac{4}{5} \right)^{(c-1)} \) represent?

Back

This represents a geometric sequence where 7 is the first term and \( \frac{4}{5} \) is the common ratio.