MathematicsGrade 11en

📐 Arithmetic and Geometric Sequences

Master the foundations and advanced concepts of arithmetic and geometric sequences, including explicit formulas, sum calculations, and real-world applications. **What you'll learn:** - Identify and classify arithmetic and geometric sequences - Derive and apply explicit and recursive formulas - Calculate partial and infinite sums using sequence formulas - Solve complex problems involving sequence behaviour and convergence

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Questions in this quiz

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Question 1
Which of the following is an arithmetic sequence?
Question 2
In the arithmetic sequence $7, 11, 15, 19, \ldots$ , the common difference is ___ and the first term is ___.
Question 3
What is the explicit formula for the $n$ -th term of the geometric sequence $3, 6, 12, 24, \ldots$ ?
Question 4
The sum of the first $n$ terms of an arithmetic sequence is always $S_n = \frac{n}{2}(2a_1 + (n-1)d)$ .
Question 5
Find the sum of the first $10$ terms of the arithmetic sequence $5, 9, 13, 17, \ldots$
Question 6
What is the sum of the infinite geometric series $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots$ ?
Question 7
The $n$ -th term of an arithmetic sequence is $a_n = 50 - 3n$ . The common difference is ___ and the sum of the first $12$ terms is ___.
Question 8
A geometric sequence has $a_1 = 2$ and $a_4 = 54$ . What is the common ratio $r$ ?
Question 9
How many terms of the geometric sequence $1, 3, 9, 27, \ldots$ must be added to get a sum of $3280$ ?
Question 10
An arithmetic sequence has $a_5 = 23$ and $a_{12} = 51$ . What is the first term $a_1$ ?