Exponential Functions: Understanding Geometric Sequences and Finding Nth Terms, Exercises of Algebra

Download Exponential Functions: Understanding Geometric Sequences and Finding Nth Terms and more Exercises Algebra in PDF only on Docsity! FOA/Algebra 1 Unit 4: Exponential Functions Notes 25 Day 7 Geometric Sequences For the following patterns, find the next two numbers. Then describe the rule you are apply each time. Rule Constant Ratio ________________________________ ______________ b. 192, 96, ________________________________ ______________ ________________________________ ______________ ________________________________ ______________ What did you notice about all of your patterns? ______________________________________________________ Sequences A sequence is a pattern involving an ordered arrangement of numbers, geometric figures, letters, or other objects. A sequence, in which you get the next consecutive term by multiplying or dividing a constant is called a geometric sequence constant value is called the constant ratio. What you may not realize is when it comes to geometric sequences is that they are considered exponential functions. The position of each term is called the term number or term position. We can think of the term number or position as the input (domain) and the actual term in the sequence as the output (range). Instead of using x for the input, we are going to use n and instead of using y for the output, we are going to use an. Term Number (n) Term (an) 1 6 36 Explicit Formula for Geometric Sequences Explicit Formula: an = a1 rn-1 1st Term Constant Ratio nth Term FOA/Algebra 1 Unit 4: Exponential Functions Notes 26 Why We Have a Formula for Sequences Take a look at the following pattern: What is the 3rd term? _________ What is the 5th term? _________ What is the 7th term? ________ What is the pattern? _________________________________________ What is the 1st term? ________ What is the 54th multiply ____ over and over 54 times?!?!?!?) This is why the Explicit Formula was created as long as you know your constant ratio and 1st term, you can create a rule to describe any geometric sequence and use it to find any term you want. Creating an Explicit Rule 1. Write down the Explicit Formula. 2. Substitute the first term in for a1 and constant ratio in for r. 3. To find an nth term, substitute the term number you are wishing to find into n. Write an Explicit Rule for the following sequences: c. 40, 10, a1 = _______ a1 = _______ a1 = _______ d = _______ d = _______ d = _______ Rule: ____________________ Rule: ____________________ Rule: ____________________ d. -1, 3, - f. -2, -12, -72 a1 = _______ a1 = _______ a1 = _______ d = _______ d = _______ d = _______ Rule: ____________________ Rule: ____________________ Rule: ____________________