Finite Geometric Series

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Presentation transcript:

Finite Geometric Series

Vocabulary: Geometric Series: is an indicated sum of terms of a geometric sequence. Example – add the first 5 terms in this sequence 1, 2, 4, 8, 16, … nth partial sum: is the sum Sn of the first n terms in a sequence Sn = 1+2+4+8+16 = 31

Example 1: Consider the sequence 31 + 32 + 33 + 34 + 35 Find This is a finite geometric series sn = g1 + g2 + g3 + g4 + g5 The sum of a finite geometric series with first term g1 and a constant ratio of r is given by:

Example 1, cont.: First, add 31 + 32 + 33 + 34 + 35 = _______ Now use the formula to find :

Example 2: Find

Example 3: You have 2 children, each of them have 2 kids, etc. How many generations until you have 1000 descendants?

Closure Find the sum of the first ten terms in the geometric series: -3, 9, -27, 81, … Find the sum for the following: