Algebra 2 Arithmetic and Geometric Sequences and Series Quiz: 10 Questions with Explanations

A 4B -3C 5D -4

Each term is 4 less than the previous one: 5 – 9 = -4.

A 8B 4C 5D 2

10 ÷ 2 = 5 and 50 ÷ 10 = 5.

A 39B 43C 40D 34

a_10 = 3 + 9(4) = 39. Using 10 instead of n – 1 would give 43.

A \(\frac{1}{2}\)B \(2\)C \(-32\)D \(\frac{1}{32}\)

Each bar is half of the one above, so r = 1/2.

A 1,250B 1,275C 2,550D 1,300

S = 50(1 + 50)/2 = 1,275.

A 243B 121C 120D 81

S_5 = (1 – 3^5)/(1 – 3) = (-242)/(-2) = 121.

A \(a_{1} = 4, \ a_{n} = a_{n-1} + 4\)B \(a_{1} = 2, \ a_{n} = 4a_{n-1}\)C \(a_{1} = 4, \ a_{n} = 2a_{n-1}\)D \(a_{n} = 4n\)

Each term is double the previous term, so multiply by 2.

A GeometricB NeitherC BothD Arithmetic

Equal steps in n add the same amount, so the graph is linear and the sequence is arithmetic.

A All real numbersB The positive integersC The nonnegative real numbersD The integers

The terms are labeled by their position n = 1, 2, 3, and so on.

A 15B 10C 20D 25

5 + 4 + 3 + 2 + 1 = 15 = 5(5 + 1)/2.