Sequences & Series

Geometric SeriesChoiRecall: What is a Series?A series is the sum of terms of a sequence.

The sum of the first n terms in a sequence is denoted as Sn.

S5 the sum of the first 5 terms

Geometric SeriesRecall: A sequence like 2, 6, 18, 54,, is called a Geometric sequence with a = 2 and r = 3.Therefore a series that corresponds to this geometric sequence is 2 + 6 + 18 + 54 +, is called a geometric series.

Geometric Series FormulaThe Sum of the First n terms of a Geometric Series

Recall: Geometric Sequence formula

Multiply this series by r

Subtract this two rows

Formula 1

or

Formula 2(Optional)

All the terms except the first and last are cancelled out

Example 1 Sum of a Series given the first termFind the sum of the first 9 terms of the geometric series.

Example 2 Sum of a Series given the first termFind the sum of the first 14 terms of the geometric series.

Example 3 Sum of a series given first and last terms Find the sum of the geometric series 5 + 20 + 80 + ... + 20480.

7

There are 7 terms in the series.

7

Example 4 Word Problem A tennis tournament has 128 entrants. A player is dropped from the competition after losing one match. Winning players go on to another match. What is the total number of matches that will be played in this tournament?

7

7

Since there are 2 players/match, the first termHalf of the players drop out because they lost.Since there will be a single match played at the end of the tournament, the last term is 1.

Therefore a total of 127 matches will be played in this tournament.Homework:Check the website