Arithmetic and Geometric Sequences Test – Algebra 1 Math (Printable PDF)

Question 1 Classify the sequences (2 points)

Classify each sequence and name its common difference or ratio. (a) 9, 16, 23, 30, … (1 point) (b) 5, 20, 80, 320, … (1 point)

Question 2 Recursive terms (2 points)

A sequence has a₁ = −4 and a_n = a_{n − 1} + 9. Write the first five terms.

Question 3 Explicit arithmetic (2 points)

Give a rule for the nth term of 21, 17, 13, 9, … and evaluate a₁₅.

Question 4 Explicit geometric (2 points)

Give a rule for the nth term of 2, −6, 18, −54, … and evaluate a₆.

Question 5 Sequence graph (3 points)

Dots on the grid mark the opening values of a sequence.

(a) Is it arithmetic or geometric? (1 point) (b) Write a formula for the nth term. (1 point) (c) Compute a₃₀. (1 point)

Question 6 Two known terms (3 points)

For an arithmetic sequence, a₄ = 23 and a₉ = 58. (a) Determine d. (1 point) (b) Determine a₁. (1 point) (c) Write its rule for the nth term. (1 point)

Question 7 Growing fund (3 points)

A fund starts at $2,400 in year 1 and grows by 5% each year, so a_n = 2,400(1.05)^{n − 1}. (a) State the common ratio. (1 point) (b) Find the value in year 4 to the nearest cent. (1 point) (c) Write a recursive formula. (1 point)

Question 8 Theater seating (3 points)

The seating chart shows the start of a pattern.

(a) Write a formula for the seats in row n. (1 point) (b) Count the seats in row 20. (1 point) (c) Which row has 70 seats? (1 point)