Sequences and Series Review

Front

What is the Binomial expansion of (x + 1)⁵?

Back

x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

Front

How do you find the total number of seats in a theater with a pattern of increasing seats per row?

Back

Identify the first term (26), the common difference (4), and use the formula for the sum of an arithmetic series.

Front

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

Back

S_n = n/2 * (a + l) where S_n is the sum, n is the number of terms, a is the first term, and l is the last term.

Front

Calculate the sum of the series: 3 + 3.3 + 3.6 + 3.9 + ... + 63.

Back

The sum is 6633.

Front

What is the common difference in the series: 3 + 3.3 + 3.6 + ...?

Back

The common difference is 0.3.

Front

Find the sum of the series: 90 + 84 + 78 + ... + 24.

Back

The sum is 684.

Front

What is the first term and common difference in the series: 90, 84, 78, ...?

Back

First term is 90, common difference is -6.

Front

Write in summation notation: 3 + 6 + 9 + 12 + ... + 30.

Back

Σ(3n) for n=1 to 10.

Front

What is the nth term formula for the series: 3, 6, 9, ...?

Back

a_n = 3n where n is the term number.

Front

Define a geometric series.

Back

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