Presentation on theme: "Aim: What is the geometric sequence?"— Presentation transcript:
1 Aim: What is the geometric sequence? Do Now: Find the first 5 numbers in a sequence whose nth term is 2n.2, 4, 8, 16, 32HW: p.269 # 4,6,8,16,18,20,28,30,32,34
2 This sequence is called a geometric sequence 2, 4, 8, 16, 32Each term of the sequence is formed by multiplying the pervious term by 2, or we could say that the ratio of each term to the previous term is a constant,2.This sequence is called a geometric sequenceA geometric sequence is a sequence such that for all n, there is a constant r such thatThe constant r is called common ratioThe common ratio of the sequence 2,4,8,16,32 is 2.
3 The recursive formula of geometric sequence is an = a1rn-1 When the geometric sequence is written in terms of a1 and r, the terms of a geometric sequence are:The recursive formula of geometric sequence is an = a1rn-1Is the sequence 4,12,36,108,324,… a geometric sequence?The ratio of any two consecutive terms is always 3, therefore the sequence is a geometric sequence with common ratio = 3
4 Write the first five terms of the geometric sequence whose first term is a1 = 3 and whose common ratio is r = 2.a1 = 3, a2 = 6, a3 = 12, a4 = 24, a5 = 48Find the 12th term of the geometric sequence whose first three terms are 5, 15,
5 Find the 15th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05. 39.599The 4th term of a geometric sequence is 125, and the 10th term is 125/64. Find the 14th term.125/1024
6 We already knew the arithmetic mean between any two terms is the average of the two terms. The geometric mean between any two terms is the square root of the product of the two terms.The geometric mean between 4 and 100 is
7 Find four geometric means between 5 and 1215 This question can be rewritten as if the 1st and 6th terms of a geometric sequence are 5 and find the 2nd, 3rd, 4th and 5th terms.We want to find the missing terms in the sequence 5, a2, a3, a4, a5, use the formula to determine the common ratio r15, 45, 135 and 405