Mathematics
Grade 10
15 min
Arithmetic sequences with fractions
Arithmetic sequences with fractions
What you'll learn
- Identify the common difference in arithmetic sequences that include fractions, given at least three consecutive terms, with 80% accuracy.
- Solve for a missing term in an arithmetic sequence with fractions, given the first term and the common difference, with 75% accuracy.
- Explain, using pictures, numbers, or words, how to find the next three terms in an arithmetic sequence with fractions.
- Apply the concept of arithmetic sequences with fractions to solve real-world problems involving patterns of fractional increases or decreases.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify if a sequence of fractional angles forms an arithmetic sequence.
Calculate the common difference (as a fraction) in an arithmetic sequence of angles, including those in radian measure.
Determine the nth term (a specific angle) in an arithmetic sequence using the formula a_n = a_1 + (n-1)d.
Calculate the sum of a finite arithmetic sequence of fractional angles, such as the interior angles of a polygon.
Solve for the first term, common difference, or number of terms in problems involving angles in polygons.
Apply the concept of arithmetic sequences to rotational angles on the unit circle using radian measures.
Ever noticed how a spiral staircase is built from steps that turn at the exact same angle each time? 📐 That's an arithmetic sequence i...
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Key Concepts & Vocabulary
TermDefinitionExample
Arithmetic SequenceA sequence of numbers where the difference between consecutive terms is constant. In this context, the 'numbers' are angle measures.The sequence of angles 90°, 97.5°, 105°, 112.5°, ... is an arithmetic sequence because you add 7.5° (or 15/2°) each time.
Common Difference (d)The constant fractional amount added to each term to get the next term. It can be positive or negative.In the sequence of radian measures π/2, π/3, π/6, 0, ..., the common difference is d = π/3 - π/2 = 2π/6 - 3π/6 = -π/6.
Term (a_n)An individual angle measure in a sequence. a_1 is the first angle, a_n is the nth angle.In the sequence 100°, 104.5°, 109°, ..., the third term is a_3 = 109°.
Interior Angles of a PolygonThe angles on the inside of a polygon formed by adjace...
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Core Formulas
nth Term of an Arithmetic Sequence
a_n = a_1 + (n-1)d
Use this formula to find the measure of a specific angle (a_n) in a sequence, given the first angle (a_1), its position in the sequence (n), and the common difference (d).
Sum of a Finite Arithmetic Sequence
S_n = n/2 * (a_1 + a_n)
Use this formula to find the sum of the first n angles in a sequence when you know the first angle (a_1), the last angle (a_n), and the number of angles (n).
Alternative Sum Formula
S_n = n/2 * (2a_1 + (n-1)d)
Use this when you need to find the sum of angles but do not know the last angle (a_n). It is particularly useful for solving for an unknown variable like 'd' or 'a_1'.
Sum of Interior Angles of a Polygon
Sum = (n-2) * 180°
A fundamental geometric rule t...
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Sign Up Free to ContinueSample Practice Questions
Easy
What is the common difference (d) in the sequence of angles: 110.5°, 108°, 105.5°, 103°, ...?
A.2.5°
B.5/2°
C.-5/2°
D.-2°
Easy
As mentioned in the tutorial, what is the common difference (d) for the sequence of radian measures π/2, π/3, π/6, 0, ...?
A.π/6
B.-π/6
C.π/3
D.-π/3
Easy
Which of the following sequences of angles forms an arithmetic sequence?
A.10°, 40/3°, 50/3°, 20°
B.π/8, π/4, 3π/8, π/2
C.100°, 50°, 25°, 12.5°
D.π, π/2, π/3, π/4
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Frequently asked questions
What grade level is "Arithmetic sequences with fractions"?
Arithmetic sequences with fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Arithmetic sequences with fractions?
You'll be able to: Identify the common difference in arithmetic sequences that include fractions, given at least three consecutive terms, with 80% accuracy; Solve for a missing term in an arithmetic sequence with fractions, given the first term….
Is "Arithmetic sequences with fractions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Arithmetic sequences with fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.