# Arithmetic and Geometric Sequences Arithmetic Sequences Every day

• Slides: 20

Arithmetic and Geometric Sequences

Arithmetic Sequences Every day a radio station asks a question for a prize of \$150. If the 5 th caller does not answer correctly, the prize money increased by \$150 each day until someone correctly answers their question.

Arithmetic Sequences Make a list of the prize amounts for a week (Mon - Fri) if the contest starts on Monday and no one answers correctly all week.

Arithmetic Sequences • Monday : • Tuesday: • Wednesday: • Thursday: • Friday: \$150 \$300 \$450 \$600 \$750

Arithmetic Sequences • These prize amounts form a sequence, sequence more specifically each amount is a term in an arithmetic sequence To find the next term we just add \$150.

What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. 4, +4 +4 8, 12 , 16, 20…………. .

What is the common difference? The difference between each number. This determines what is added to each previous number to obtain the next number. 4, 8, 12, 16, 20…………. . 4 is the common difference

Geometric Sequence • What if your pay check started at \$100 a week and doubled every week. What would your salary be after four weeks?

Geometric. Sequence • • • Starting \$100. After one week - \$200 After two weeks - \$400 After three weeks - \$800 After four weeks - \$1600. These values form a geometric sequence.

What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. x 3 3, x 3 x 3 9, 27 , 81, 243…………. .

What is the common ratio? The number used to multiply by each previous number to obtain the next number. 2, 8, 32, 128, 512…………. . 4 is the common ratio

Let’s Practice!

Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference

Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2, 592…… Geometric Sequence x 6 6 is the common ratio

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? x 4 x 4 5, 20, 80, 320 , _____ 1, 280

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? -6 -6 5, -1, -7 -13 , _____ -19

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? X-2 X-2 -3, 6, -12, 24 , _____ -48

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? +20 +20 -400, -380, -360, -340 , -320 ____

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? -25 -25 100, 75, 50 , 25____ 0

Is this an arithmetic or geometric sequence? What is the common ratio or difference? What is the next term in this sequence? x-4 x-4 -48, 192 , -768____ x-4 12, 3, 072