Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
The last six problems model situations such as savings, seating, social media, depreciation, toothpick patterns and a bouncing ball (F-LE.A.2).
Standards: F-IF.A.3, F-BF.A.2, F-LE.A.2 · Level: Grade 9 Algebra 1
Problem 1 Common difference ★★★
Find the common difference of 7, 13, 19, 25, … and the next term.
Problem 2 Common ratio ★★★
Find the common ratio of 6, 30, 150, 750, … and the next term.
Problem 3 List an arithmetic sequence ★★★
Write the first five terms when a1 = 12 and d = −4.
Problem 4 List a geometric sequence ★★★
Write the first four terms when a1 = 2 and r = 5.
Problem 5 Classify sequences ★★★
Sort each list into arithmetic, geometric, or neither: (a) 4, 9, 16, 25 (b) 24, 12, 6, 3 (c) 11, 8, 5, 2.
Problem 6 Formula from a graph ★★★
Four dots on the graph begin an arithmetic sequence. Find a formula for the nth term, then compute a20.
Problem 7 Explicit arithmetic formula ★★★
Give a rule for the nth term of 15, 11, 7, 3, … and evaluate a12.
Problem 8 Explicit geometric formula ★★★
Give a rule for the nth term of 6, 18, 54, … and evaluate a6.
Problem 9 Recursive to explicit ★★★
A sequence has a1 = 9 and an = an − 1 + 5. List the first five terms and write an explicit formula.
Problem 10 Recursive geometric ★★★
For the sequence 80, 40, 20, 10, … write a recursive formula and find a8.
Problem 11 Which term equals 128? ★★★
In the arithmetic sequence 8, 14, 20, … which term equals 128?
Problem 12 Two terms of an arithmetic sequence ★★★
Two terms of an arithmetic sequence are known: a3 = 17 and a7 = 37. Determine d, a1 and a rule for the nth term.
Problem 13 Two terms of a geometric sequence ★★★
In a geometric sequence, a2 = 12 and a5 = 324. Determine r and a1.
Problem 14 Sequence as a function ★★★
The dots on the graph are the opening values of f(n). Identify the common ratio, write the rule for f(n) and compute f(5).
Problem 15 Weekly savings ★★★
Mia saves $15 in week 1 and adds $8 more each week than the week before, so she saves $15, $23, $31, … in successive weeks. Write a formula for week n and find the first week she saves more than $150.
Problem 16 Stadium rows ★★★
Row 1 of a section has 22 seats and every later row has 3 more than the one in front. Count the seats in row 30 and name the row with 70 seats.
Problem 17 Viral video views ★★★
A video gets 3 views on day 1, and the number of views triples each day. Write a formula for day n, find the views on day 7 and the first day with more than 10,000 views.
Problem 18 Two depreciation models ★★★
A car is worth $18,000 in year 1. Model A loses 20% of its value each year. Model B loses $2,500 each year. Compare the values in year 4 and write a recursive formula for Model A.
Problem 19 Toothpick squares ★★★
Toothpicks build a row of squares. Write a formula for the toothpicks needed for n squares, then find the count for 25 squares and the number of squares made from 100 toothpicks.
Problem 20 Bouncing ball ★★★
A ball is dropped from 160 inches. Each bounce reaches 75% of the previous height. Write a formula for the height after bounce n, find the height after bounce 5 to the nearest hundredth, and the first bounce lower than 20 inches.
