Algebra 1 Arithmetic and Geometric Sequences Quiz: 10 Questions with Explanations

A 26B 31C 27D 29

The common difference is 4, so the next term is 23 + 4 = 27.

A 6B 3C 16D 4

Divide each term by the one before: 8/2 = 4. The differences 6, 24, 96 are not constant.

A \(a_{n} = 3n + 2\)B \(a_{n} = 3n + 5\)C \(a_{n} = 5n + 3\)D \(a_{n} = n + 3\)

With a1 = 5 and d = 3, a_n = 5 + 3(n – 1) = 3n + 2.

A \(a_{n} = 2n + 1\)B \(a_{n} = 2n – 1\)C \(a_{n} = n + 2\)D \(a_{n} = 2^{n}\)

The terms are 1, 3, 5, 7, so d = 2 and a_n = 1 + 2(n – 1) = 2n – 1.

A \(a_{1} = 20, a_{n} = a_{n-1} – 3\)B \(a_{1} = 20, a_{n} = a_{n-1} + 3\)C \(a_{1} = 20, a_{n} = 3a_{n-1}\)D \(a_{1} = 3, a_{n} = a_{n-1} – 20\)

Each term is 3 less than the one before it.

A 30B 486C 162D 54

a5 = 2 · 3^4 = 2 · 81 = 162. Using 3^5 gives 486.

A \(4, 12, 36, 108\)B \(4, 8, 12, 16\)C \(4, 6, 9, 13\)D \(4, 12, 20, 28\)

Only 4, 12, 36, 108 has a constant ratio of 3. The others have constant or changing differences.

A 16B 19C 22D 18

The rule is a_n = 3n + 1, so Figure 6 has 3(6) + 1 = 19 squares.

A 2,000B 1,500C 8,000D 4,000

a4 = 500 · 2^3 = 4,000. Doubling 4 times instead of 3 times gives 8,000.

A Arithmetic with difference 6B Geometric with ratio 2C Geometric with ratio 6D Arithmetic with difference 2

Each term is double the previous one, so the common ratio is 2.