Which of the following are geometric sequences?

Question

1,1,2,3,5,8,13

5,10,15,20,25

-9,-3,-1,-1/3,-1/9,-1/27

10,5,2.5,1.25,0.625,0.3125

Answer 1

One of the easiest ways to check for a geometric sequence is to see if the ratio is the same between elements.

With your first sequence 1,1,2,3,5,8,13 - you take the second element and divide it by the first 1/1 = 1, now we take the third element and divide it by the second 2/1 = 2. Since the ratio is not the same, it is not a geometric sequence.

Your second sequence 5,10,15,20,25 is also not a geometric sequence because 10/5 = 2 and 15/10 = 3/2.

Your third sequence -9,-3,-1,-1/3,-1/9,-1/27 is a geometric sequence because -3/-9 = 1/3 and -1/-3 = 1/3.

Your last sequence 10,5,2.5,1.25,0.625,0.3125 is a geometric sequence because 5/10 = 1/2 and 2.5/5 = 1/2.

Answer 2

The first example is the Fibonacci sequence, where each value is the sum of the two preceding values.

Second is arithmetic; the difference is always 5.

Third and fourth are geometric. The ratio of adjacent values is 1/3 and 1/2 respectively.

Answer 3

Look at the last two sequences

Starting with -9 divide each number by positive 3 to get the next number

-9, -3, -1, -1/3, -1/9, -1/27

-9/3 = -3

-3/3, = -1

-1/3 = -1/3

-1/3÷ 3= -1/9

-1/9÷3 = -1/27

starting with 10 divide each number by two to get the next number

10, 5, 2.5, 1.25, 0.625, 0.3125

10/2 = 5

5/2 = 2.5

2.5/2 = 1.25

1.25/2 = 0.625

0.625/2 = 0.3125

The second sequence

5, 10, 15, 20, 25 looks like arithmetic

5+5 =10

10+5 =15

15+5 = 20

20+5 = 25

Hope this helps