Question

Sort the sequences to whether they are arithmetic, geometric, or neither
1) 98.3 , 94.1 , 89.9 , 85.7
2) 1 ,0 , -1 ,0
3) 1.75 , 3.5 , 7 ,14
4) -1 ,1 , -1 ,1
5) -12, -10.8, -9.6, -8.4

Answer 1

her answer is right but you just have to switch 4 and 5 around 4 is geometric while 5 is arithmetic

Answer 2

1)  The sequence is an arithmetic sequence.

2) They have neither a common difference nor a common ratio.

3) The sequence is an arithmetic sequence.

4) The sequence is a geometric sequence.

5) The sequence is an arithmetic sequence.

Sequences are numbers arranged in a particular pattern.

Arithmetic sequences are separated by a common difference while geometric sequences are separated by a common ratio.

Given the sequence T1, T2, T3...

If the sequence is an arithmetic sequence;

d = T2 - T1 = T3 - T2

If the sequence is a geometric progression:

$r=\frac{T_3}{T_2} =\frac{T_2}{T_1}$

Given the sequence

1) 98.3 , 94.1 , 89.9 , 85.7

d = 94.1 - 98.3 = 89.9 - 94.1

d = -4.2

Since they have the same common difference, the sequence is an arithmetic sequence.

2) 1 ,0 , -1 ,0

For the sequence, it is neither arithmetic sequence nor geometric sequence since they have neither a common difference nor common ratio.

3) For the sequence  1.75 , 3.5 , 7 ,14

r = 3.5/1.75 = 7/3.5 = 14/7 = 2

Since the sequence has a common ratio, the sequence is a geometric sequence

4) For the sequence -1 ,1 , -1 ,1

r = 1/-1 = -1/1 = 1/-1 = -1

Since the sequence has a common ratio of -1, the sequence is a geometric sequence.

5) Given the sequence  -12, -10.8, -9.6, -8.4

d = -10.8+12 = -9.6+10.8 = -8.4+9.6

d = 1.2

Since they have the same common difference, the sequence is an arithmetic sequence.

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