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Calculus

Sequences and Series

Concept Quizzes

Sequences Warmup
Visual Patterns
Finding the nth Term
Arithmetic Progressions
Geometric Progressions
Arithmetic Progression Sum
Geometric Progression Sum
Finite Series
Telescoping Series - Sum
Sequences and Series - Problem Solving
Calculus Introduction 4

Challenge Quizzes

Sequences and Series: Level 1 Challenges
Sequences and Series: Level 3 Challenges
Sequences and Series: Level 4 Challenges

Sequences Warmup

If $\{a_n\}$ is a sequence defined by $a_n = n^2 + n + 1$ for each natural number $n$ , what is $a_5?$

21 25 30 31

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by Brilliant Staff

Suppose $\{a_n\}$ is a sequence defined by $a_1 = 1, a_2 = 1,$ and $a_n = a_{n-1} + a_{n -2}$ for each natural number $n > 2.$

What is $a_6$ ?

8 13 20 21

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by Brilliant Staff

A geometric progression is a sequence in which $a_n = r \cdot a_{n-1}$ for each natural number $n > 1$ , where $r$ is a real number called the common ratio.

If $a_n$ is a geometric progression with $a_1 = 5$ and $a_6 = 160$ , what is $a_3$ ?

20 25 45 62

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by Brilliant Staff

On Day 1, Isabel has $200 in the bank, and she adds $5 at the start of each subsequent day. On what day will her account’s value reach $300?

21 100 20

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by Brilliant Staff

Each day this week, Morgan had twice as much money as the day before. On Day 6, Morgan had $40. How many dollars did Morgan have on Day 1?

5 2.50 1280 1.25

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by Brilliant Staff

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