The document discusses geometric sequences and provides examples of determining if a series of numbers forms a geometric sequence. It defines a geometric sequence as one where each term after the first is obtained by multiplying the preceding term by a fixed number called the common ratio. Examples are provided of finding common ratios and future terms in geometric sequences like -5, 10, -20, ... The document also covers calculating the geometric mean of consecutive terms in a geometric sequence.

1. GRADE 10 MATHEMATICS

2. LET US REVIEW

3. A Sequence in which each term after the first is
obtained by multiplying the preceding term by a
fixed number called the common ratio, denoted
by r
Example: Determine if the following is a geometric
sequence, arithmetic sequence, or neither.
• 7, 14, 28, 56, ...
• 11, 13, 15, 17, ...
• 1, 1, 2, 3, 5, ...

4. The rule for geometric
sequence is: Examples:
• Given the
sequence 5, 10, 20,
... find a8
• Given 2, -6, 18, ...
find a6
• Find the common
ratio and the next
three terms of 6,
18, 48, ...

5. Answer on your notebook.
Show complete solutions.
Find the common ratio and
a7 in the sequence -5, 10, -
20, ...

6. The geometric mean of any two consecutive terms of
a geometric sequence is the square root of their
product.
Geometric mean = ± √ab; where a and b are
consecutive terms of a geometric sequence.
Examples:
• Find the geometric mean between 2 and 18.
• Find the three geometric means between -2 and
-162.

7. Answer Activity Sheet #3.