Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Early problems build fluency with rules and terms. The last six use seating, savings, salary, bouncing balls and loans, so keep units and rounding in mind.
Standards: A-SSE.B.4, F-BF.A.2, F-IF.A.3 · Level: Grade 11 Algebra 2
Problem 1 Classify the sequence ★★★
Decide whether 14, 9, 4, −1, … is arithmetic or geometric. Give the common difference or ratio and the next term.
Problem 2 Explicit rule from a first term ★★★
An arithmetic sequence has first term 11 and common difference 6. Write the explicit rule and find a12.
Problem 3 Find the common ratio ★★★
Find the common ratio and the next term of 405, 135, 45, …
Problem 4 List terms from a recursive rule ★★★
A sequence is defined by a1 = 3 and an = 2an−1 + 1. Write the first five terms.
Problem 5 Arithmetic term from two terms ★★★
In an arithmetic sequence a4 = 17 and a9 = 42. Find a1, d and a30.
Problem 6 Geometric term ★★★
Find a7 of the geometric sequence 12, 18, 27, …
Problem 7 Evaluate a sigma sum ★★★
Evaluate ∑k=15 (3k − 2) by writing out the terms.
Problem 8 Geometric sigma sum ★★★
Evaluate ∑k=16 2 · 3k−1.
Problem 9 Sum of an arithmetic series ★★★
Find the sum 6 + 10 + 14 + … + 70.
Problem 10 Alternating geometric series ★★★
Find the sum of the first 5 terms of 8 − 12 + 18 − 27 + …
Problem 11 Write sigma notation ★★★
Write 4 + 7 + 10 + … + 40 in sigma notation.
Problem 12 Rule from a graph (arithmetic) ★★★
The graph shows the first four terms of an arithmetic sequence. Write the explicit rule.
Problem 13 Rule from a graph (geometric) ★★★
The graph shows a geometric sequence. Find r and write the explicit rule.
Problem 14 Number of terms ★★★
How many terms are in the geometric sequence 3, 6, 12, …, 1536?
Problem 15 Theater seating ★★★
A theater has 18 seats in row 1, and each later row has 3 more seats than the row before. The bars show the first five rows. How many seats are in row 22, and how many seats are in all 22 rows?
Problem 16 Monthly savings plan ★★★
Mina deposits $200 at the end of each month into an account that earns 0.5% per month. Use the sum of a geometric series to find the balance after 24 deposits.
Problem 17 Salary with yearly raises ★★★
A job pays $42,000 the first year and the pay rises 3% each year. Find the total pay over the first 10 years, to the nearest dollar.
Problem 18 Bouncing ball heights ★★★
A ball dropped from 6 feet rebounds to 75% of its previous height after each bounce. Find the height after the 5th bounce, and write the recursive rule for the rebound height (heights in the graph are rounded).
Problem 19 Car loan payment ★★★
A $15,000 loan at 6% annual interest is repaid in 48 equal monthly payments. The payment is M = Pr/(1 − (1 + r)−n), where r is the monthly rate. Find M.
Problem 20 Sum of odd numbers ★★★
Show that the sum of the first n odd numbers 1 + 3 + 5 + … is n2, then use it to find 1 + 3 + 5 + … + 49.
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