Chapter 10 Review: Sequences and Series

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

Front

Identify the common difference in the arithmetic sequence: 4, 6, 10, 12, 16.

Back

The common difference is 2.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term (t(n)) can be found using the formula: t(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What is a geometric series?

Back

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

Front

How do you find the sum of the first n terms of a geometric series?

Back

The sum S(n) of the first n terms can be calculated using the formula: S(n) = a(1 - r^n) / (1 - r), where 'a' is the first term and 'r' is the common ratio.

Front

What is the formula for the sum of an arithmetic series?

Back

The sum S(n) of the first n terms of an arithmetic series can be calculated using the formula: S(n) = n/2 * (a + l), where 'a' is the first term, 'l' is the last term, and 'n' is the number of terms.

Front

Find the 22nd term of the arithmetic sequence: 5, 8, 11, ...

Back

The 22nd term is 68.

Front

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

Back

The sum is -29524.

Front

How do you determine the total number of cans in a stacked arrangement?

Back

To find the total number of cans in a stacked arrangement, sum the number of cans in each row, which decreases by one can per row.

Front

If t(1) = 22 and d = -8, find t(21).

Back

t(21) = -1218.