Arithmetic and Geometric Sequences: Algebra 1 Math Worksheet – PDF Download

Problem 1: Arithmetic: next terms

The sequence \(5,9,13,17\) is arithmetic. Find the common difference and the next two terms.

Problem 2: Geometric: next terms

Find the common ratio of \(4,12,36,108\) and the next two terms.

Problem 3: Decreasing arithmetic

Find the next three terms of the arithmetic sequence \(50,43,36\).

Problem 4: A ratio less than 1

Find the common ratio and the next three terms of the geometric sequence \(80,40,20\).

Problem 5: Arithmetic, geometric or neither

Classify each sequence as arithmetic, geometric, or neither. Give the common difference or ratio when there is one.

1. \(2,4,8,14\)
2. \(1,-2,4,-8\)
3. \(10,5,0,-5\)

Problem 6: Explicit rule: arithmetic

Write an explicit formula for the arithmetic sequence \(6,11,16,21\) and use it to find the 20th term.

Problem 7: Explicit rule: geometric

Write an explicit formula for the geometric sequence \(5,10,20,40\) and find the 8th term.

Problem 8: Recursive: arithmetic

Write a recursive formula for the arithmetic sequence \(20,17,14,11\), then find \(a_{6}\).

Problem 9: Recursive: geometric

Write a recursive formula for the geometric sequence \(1.5,3,6,12\), then find \(a_{7}\).

Problem 10: Use a_1 and d

An arithmetic sequence has \(a_{1}=-8\) and \(d=6\). Write the explicit formula and find \(a_{15}\).

Problem 11: From a recursive rule

A sequence is defined by \(a_{1}=4\) and \(a_{n}=3\cdot a_{n-1}\) for \(n\ge 2\).

1. List the first five terms.
2. Write an explicit formula and use it to verify \(a_{5}\).

Problem 12: Find the rule from two terms

An arithmetic sequence has \(a_{3}=11\) and \(a_{7}=27\). Find the common difference, \(a_{1}\) and the explicit formula.

Problem 13: Geometric from two terms

A geometric sequence has \(a_{2}=6\) and \(a_{5}=162\). Find the common ratio, \(a_{1}\) and the explicit formula.

Problem 14: Which term?

In the arithmetic sequence \(4,10,16,22\), which term equals 154?

Problem 15: Sequence from a graph

The graph shows the first four terms of a sequence.

1. List the terms and decide whether the sequence is arithmetic or geometric.
2. Write an explicit formula and find \(a_{8}\).

Problem 16: Decay by a third

A geometric sequence has \(a_{1}=243\) and \(r=\frac{1}{3}\). Find \(a_{6}\) with the explicit formula.

Problem 17: Weekly savings

Liam puts $15 in a jar in week 1 and adds $6 more each week, so the amount he deposits is an arithmetic sequence.

1. Write an explicit formula for the amount \(a_{n}\) he deposits in week \(n\).
2. How much does he deposit in week 12?
3. In which week does the deposit first exceed $100?

Problem 18: Doubling views

A video gets 50 views on day 1, and the number of views each day is double the day before.

1. Write a recursive formula and an explicit formula for the views \(a_{n}\) on day \(n\).
2. How many views does the video get on day 7?

Problem 19: Stadium rows

The first row of a section in a Little League stadium has 18 seats, and each row behind it has 2 more seats than the row in front.

1. Write an explicit formula for the number of seats in row \(n\).
2. How many seats are in row 25?
3. Which row has exactly 50 seats?

Problem 20: Car depreciation

A new car is worth $20,000. Each year its value drops by 15% of the value the year before. Let \(a_{n}\) be its value at the start of year \(n\), so \(a_{1}=20000\).

1. Write an explicit formula for \(a_{n}\).
2. Find the value at the start of year 4.
3. At the start of which year does the value first fall below $10,000?

Problem 21: Two growth plans

Plan A starts with $100 and adds $25 each month. Plan B starts with $10 and doubles each month. Let \(n\) be the month number, with month 1 as the starting amount.

1. Write an explicit formula for each plan.
2. In which month does Plan B first exceed Plan A?

Problem 22: Bouncing ball

A ball reaches 16 feet on its first bounce. Each later bounce reaches \(\frac{3}{4}\) of the height of the bounce before it.

1. Write an explicit formula for the height \(a_{n}\) of bounce \(n\).
2. How high is the 4th bounce?

⬇ Download the Algebra 1 Arithmetic and Geometric Sequences worksheet (PDF, 81 KB)

See every chapter on the Algebra 1 math page.