Math 10 Q1

• What are the terms in an arithmetic sequence between two numbers a and b called?

  Arithmetic Means
• How is an arithmetic sequence defined?

  It is a sequence where each term after the first is obtained by adding the same constant.
• What is the constant added to each term of an arithmetic sequence called?

  Common Difference
• What is the definition of a common ratio?

  A constant multiplied to each term of a geometric sequence to obtain the next term.
• What is the Fibonacci Sequence?

  A sequence where its first two terms are either both 1, or 0 and 1, and each term thereafter is obtained by adding the two preceding terms.
• What characterizes a finite sequence?


  It is a function whose domain is the finite set {1, 2, 3, ..., n}.
• What are geometric means?

  Terms m₁, m₂, ..., m between two numbers a and b such that a, m₁, m₂, ..., m, b is a geometric sequence.
• How is a geometric sequence defined?

  It is a sequence where each term after the first is obtained by multiplying the preceding term by the same constant.
• What is a harmonic sequence?

  A sequence such that the reciprocals of the terms form an arithmetic sequence.
• What is an infinite sequence?

  It is a function whose domain is the infinite set {1, 2, 3, ...}.
• What is the definition of a term in a sequence?

  Any number in a sequence.
• When does the sum of an infinite geometric series converge to a finite value?

  When the common ratio of a geometric sequence is between -1 and 1.
• What is the formula for the sum to infinity of an infinite geometric series?


  S∞ = $\frac{a_1}{1 - r}$
• What does the formula for the sum to infinity allow you to calculate?

  It allows you to calculate the sum of an infinite geometric series when the common ratio is within the specified range.
• In the example of the infinite geometric series 1, 1/2, 1/4, 1/8..., what is the sum to infinity?

  2
• What is the general form of a geometric sequence?

  $a_n =$$a_1 \times r^{(n-1)}$
• How do you find the 8th term of the geometric sequence 3, 6, 12, 24...?

  $a_8 =$$3 \times 2^{(8-1)} =$$384$
• What is the formula for the sum of the first n terms of a geometric sequence?


  $S_n =$$\frac{a_1 (r^n - 1)}{r - 1}$
• How do you find the sum of the first 5 terms of the geometric sequence 3, 6, 12, 24...?


  $S_5 =$$3 \times \frac{(2^5 - 1)}{2 - 1} =$$93$
• How is an arithmetic sequence defined?

  It is a sequence where the difference between consecutive terms is constant.
• What is the constant difference in an arithmetic sequence called?

  Common Difference
• What is the general form of an arithmetic sequence?

  $a_n =$$a_1 +$$(n - 1)d$
• How do you find the 10th term of the arithmetic sequence 2, 5, 8, 11...?


  $a_{10} =$$2 +$$(10 - 1) \times 3 =$$29$
• What is the formula for the sum of the first n terms of an arithmetic sequence?


  $S_n =$$\frac{n}{2} [2a_1 + (n - 1)d]$
• How do you find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, 11...?


  $S_{10} =$$\frac{10}{2} [2(2) +$$(10 - 1) \times 3] =$$155$