1.4 Sequences and Series

• What is a sequence defined as?

  Ordered list of numbers
• Sequences are denoted using subscripts, while series use sigma notation.
• The formula for the nth term of an arithmetic sequence is $a_{n} =$$a_{1} +$$(n - 1)d$.


  True
• What is a key property of quadratic sequences?

  Constant second difference
• A geometric sequence is characterized by a constant common ratio.
• In an arithmetic sequence, the common difference (d) is calculated as d = a_{n} - a_{n - 1}</latex>
• How is the common ratio (r) of a geometric sequence calculated?

  r = \frac{a_{n}}{a_{n - 1}}</latex>
• What notation is used to denote a series?

  $\sum_{i = 1}^{n} a_{i}$
• In the Fibonacci sequence, each term is the sum of the two preceding terms.


  True
• What does the formula for the nth term of an arithmetic sequence allow us to calculate?

  Any term in the sequence
• The common difference in the sequence 2, 5, 8, ... is 3
• What is the common ratio in a geometric sequence called?

  r
• The nth term of a geometric sequence is given by $a_{n} =$$a_{1} \cdot r^{(n - 1)}$.


  True
• What is the 6th term of the arithmetic sequence 2, 5, 8, ...?

  17
• The 4th term of the geometric sequence 3, 6, 12, 24, ... is 24
• The formula for the nth term of a geometric sequence is $a_{n} =$$a_{1} \cdot r^{(n - 1)}$.


  True
• The common ratio and the formula for the nth term are key properties of geometric sequences.


  True
• What is the common ratio in a geometric sequence?

  The constant factor multiplied
• How are series denoted?

  Using sigma notation
• What is the common difference in the arithmetic sequence 2, 4, 6, 8, ...?

  2
• The common difference in the arithmetic sequence 2, 5, 8, 11, ... is 3
• What is the general form of a geometric sequence?

  $a, ar, ar^{2}, ar^{3}, \dots$
• An arithmetic series is the sum of the terms in an arithmetic sequence
• What is the formula to find the sum of the first n terms of a geometric series?

  $S_{n} =$$\frac{a_{1}(1 - r^{n})}{1 - r}$
• What is the formula to find the nth term of an arithmetic sequence?

  a_{n} = a_{1} + (n - 1)d</latex>
• Sequences represent the sum of terms, while series represent the ordered list of terms.

  False
• What is the common difference in an arithmetic sequence?

  Constant amount added
• What is the constant amount by which an arithmetic sequence decreases called?

  Common difference
• In a geometric sequence, each term is multiplied by a constant called the common ratio.


  True
• What is a sequence defined as?

  Ordered list of numbers
• Sequences are denoted using subscripts
• What is unique about a quadratic sequence?

  Second difference is constant
• In an arithmetic sequence, the first term is denoted as $a_{1}$
• What is the initial term in the sequence 2, 5, 8, ...?

  2
• The formula for the nth term of an arithmetic sequence allows easy calculation of any term if the first term and common difference are known.


  True
• What is the formula for the common ratio in a geometric sequence?

  $r =$$\frac{a_{n}}{a_{n - 1}}$
• In the formula for the nth term of an arithmetic sequence, $a_{1}$ represents the first term.
• What is the common ratio in the geometric sequence 3, 6, 12, 24, ...?

  2
• What is the formula to find the nth term of a geometric sequence?

  a_{n} = a_{1} \cdot r^{(n - 1)}</latex>
• For an arithmetic sequence, the common difference d is the constant value added