Arithmetic and Geometric Sequences

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

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

What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. 3, 9, 27 , 81, 243………….. x3 x3 x3 x3

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 x6 6 is the common ratio

What is the next term in this sequence? 5, 20, 80, 320 , _____ 1,280

What is the next term in this sequence? 5, -1, -7 -13 , _____ -6 -6 -6 -6 -19

What is the next term in this sequence? -3, 6, -12, 24 , _____ -48

What is the next term in this sequence? -400,-380,-360,-340 , ____ +20 +20 +20 +20 -320

What is the next term in this sequence? 100, 75, 50 , 25____ -25 -25 -25 -25

What is the next term in this sequence? 12, -48, 192 , -768____ 3,072

LETS PRACTISE

Given that arithmetic sequence: 30, 23, 16, 9, 2…… find the 15th term and the sum of the first 15 terms 2. The first three terms of a sequence are 2, b, 18. Find the positive value of b so that the sequence is a. An arithmetic progression b. A geometric progression 3. Given a, a+1, a-2 are three consecutive terms of a geometric sequence, find the value of y and the common ratio.

4. The first term of an arithmetic sequence is -8 and the last term is 70. If the common different is 5 find a. The number of the terms in the sequence b. The sum of all the terms in the sequence