PC Chapter 7 Review

Front

What is a common ratio in a geometric sequence?

Back

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

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

How do you calculate the sum of the first n terms of an arithmetic series?

Back

The sum (S_n) can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

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

Back

The sum (S_n) can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where a_1 is the first term and r is the common ratio.

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is 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

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 2 * 3^(4-1) = 2 * 27 = 54.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that is added to each term to get the next term in an arithmetic sequence.

Front

How do you find the 32nd term of the sequence 34, 37, 40, 43, ...?

Back

Using the formula for the nth term: a_n = a_1 + (n-1)d, where a_1 = 34 and d = 3, the 32nd term is 34 + (32-1)3 = 34 + 93 = 127.

Front

What is the sum of the first 10 terms of the series 2 - 6 + 18 - 54 + ...?

Back

The sum is -29524.