2nd Block Math 4 Unit 6 Review

Front

What is the formula for the sum of a geometric series?

Back

The sum of a geometric series can be calculated using the formula: $$S_n = a \frac{1 - r^n}{1 - r}$$ where \(S_n\) is the sum of the first \(n\) terms, \(a\) is the first term, and \(r\) is the common ratio.

Front

Define a geometric sequence.

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio \(r\) in a geometric sequence is the factor by which we multiply each term to get the next term. It can be found by dividing any term by the previous term.

Front

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

Back

The nth term of a geometric sequence can be found using the formula: $$a_n = a \cdot r^{(n-1)}$$ where \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

Front

What is the formula for the sum of an infinite geometric series?

Back

The sum of an infinite geometric series can be calculated using the formula: $$S = \frac{a}{1 - r}$$ where \(a\) is the first term and \(|r| < 1\) is the common ratio.

Front

What is the difference between a geometric sequence and a geometric series?

Back

A geometric sequence is a list of numbers in which each term is multiplied by a common ratio, while a geometric series is the sum of the terms of a geometric sequence.

Front

What is the value of the expression $$1 - \left(\frac{1}{6}\right)^n$$ when n=2?

Back

When \(n=2\), the expression evaluates to: $$1 - \left(\frac{1}{6}\right)^2 = 1 - \frac{1}{36} = \frac{35}{36}.$$

Front

Calculate the sum of the first 5 terms of the geometric sequence with first term 3 and common ratio 2.

Back

The sum of the first 5 terms is: $$S_5 = 3 \frac{1 - 2^5}{1 - 2} = 3 \frac{1 - 32}{-1} = 93.$$

Front

What is the formula for the nth term of a geometric sequence with first term 5 and common ratio 3?

Back

The nth term can be calculated using: $$a_n = 5 \cdot 3^{(n-1)}.$$

Front

If the first term of a geometric sequence is 4 and the common ratio is 0.5, what is the 4th term?

Back

The 4th term is: $$a_4 = 4 \cdot (0.5)^{(4-1)} = 4 \cdot 0.125 = 0.5.$$