Question

Part 1 [3 points]: Describe in detail an example of a geometric sequence.
Part 2 [4 points]: Show all steps of finding the 6th term of the sequence

Answer 1

in a geometric sequence the terms have been multiplied by the same number.... called a common ratio

an example is the sequences 1, 2, 4, 8, 16, 32, 64...... the common ratio is 2

so the 1st term is multiplied by 2 to find the 2nd, then 2nd x 2 to get 3rd etc

the common ratio can be negative which creates an alternating sequence

1, -3, 9, -27, 81, ..... common ratio -3

the common ratio can also be a fractor

256, 128, 64, 32, .... r = 1/2


the formula for a term in a common ratio is

\[T _{n} = a \times r^{n -1}\]

T is the term in position n, a = 1st term and r = common ratio