Maryland Math A.SSE.B.4.a

MathGrades 9–12SEEING STRUCTURE IN EXPRESSIONS

The Standard

A.SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.

Express the sums in a series using sigma notation.

Maryland College and Career Ready Standards for Mathematics (2025) · Write expressions in equivalent forms to solve problems.

Teacher's field guide

What Students Need to Do: Students find a rule for the terms in a finite sum. They write the sum using a sigma symbol, a term formula, and starting and ending values for the index.
What Mastery Looks Like: Given 4 + 8 + 12 + 16, a student writes ∑_{k=1}^{4} 4k. They can expand the notation to check that it produces exactly those four terms.
Common Misconceptions: Students may put 16 above the sigma because it is the last term, rather than use 4 because there are four terms. They may write 4k but start k at 0, which adds an unwanted zero term.
How to Assess It: Exit ticket: Write 5 + 10 + 15 + 20 + 25 in sigma notation. Expand your answer to check the first and last terms.

Lesson moves

Give pairs cards showing 3, 6, 9, 12 and k = 1, 2, 3, 4; have them match cards and write the sigma expression.
Ask: How do ∑_{k=1}^{4} 2k and ∑_{k=0}^{3} (2k + 2) produce the same sum? Have students expand both.
Match cards showing 1 + 4 + 9 + 16 to sigma cards; include ∑_{k=1}^{5} k² as a distractor.
A student saves $5 in week 1, $10 in week 2, and so on through week 6; write the total in sigma notation.

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