Algebra II Sequences and Series Review

Front

What is the formula for the nth term of an arithmetic sequence?

Back

a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

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

Back

S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms.

Front

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

Back

S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the difference between consecutive terms.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio (r) is the ratio of consecutive terms.

Front

Write the first 6 terms of the sequence: a_n = -2n - 5.

Back

-7, -9, -11, -13, -15, -17.

Front

Write the rule for the nth term of the sequence: -7, -4, -1, 2...

Back

a_n = 3n - 10.

Front

Find the sum of the first 6 terms of the sequence: a = 100 (1/2)^(n-1).

Back

1575/8.

Front

Describe the sequence: 1, 5, 25, 125... and find the 5th term.

Back

Geometric, a_5 = 625, a_n = 5^(n-1).