11.3 Geometric Sequences

Geometric Sequence Definition: The constant is called : Common Ratio A sequence in which the all terms after the first are found by multiplying the by a constant 2, 4, 8, 16, … (multiply each term by 2) 81, 27, 9, 3, ….. (multiply each term by 1 3 The constant is called : Common Ratio

Find the next two terms in the sequence 405, 135, 45,…. 16, 24, 36, ….

Geometric Sequence Formula: an=a1rn-1 0.05, 0.25, 1.25, 6.25, … r = .25 .05 =5, 1.25 .25 =5, 6.25 1.25 =5 an = (.05)5n - 1

Find a term given the first term and the common ratio a1 = -3 r = -2 Find the eighth term a1 = − 1 9 r = 3 Find the sixth term

Write an equation for the nth term 432, 72,12, ….

Write an equation for the nth term 72, 56, 40, 24, …

Find a term given one term and the common ratio a4 = 108 r = 3 Find the tenth term. aA3 = 16 r = 4 Find the eighth term

Geometric Means The terms between any two non-successive terms in a geometric sequence Use the formula to find the common ratio Then use the common ratio to calculate the geometric means

Find the geometric means 2.25, __, __, __, 576 Find the two geometric means between 4 and 13.5