Question

Identify the sequence as arithmetic, geometric, or neither. 1.6, 0.8, 0.4, 0.2, explain

Answer 1

Answer:

each term is half the previous one

1.6 *.5^(n-1)

is a geometric sequence

Answer 2

The sequence 1.6 , 0.8 , 0.4 , 0.2 is a geometric sequence

Given :

The sequence 1.6 , 0.8 , 0.4 , 0.2

To find :

Identify the sequence as arithmetic, geometric, or neither

Concept :

Arithmetic sequence :

A sequence of numbers are said to form an Arithmetic progression if the difference between any two consecutive terms is always the same.

Geometric sequence :

A sequence of numbers are said to form an Geometric progression if the ratio between any two consecutive terms is always the same.

Solution :

Step 1 of 3 :

Write down the terms of the sequence

The given sequence is 1.6 , 0.8 , 0.4 , 0.2

First term = a₁ = 1.6

Second term = a₂ = 0.8

Third term = a₃ = 0.4

Step 2 of 3 :

Identify the sequence is arithmetic or not

a₂ - a₁ = 0.8 - 1.6 = - 0.8

a₃ - a₂ = 0.4 - 0.8 = - 0.4

∴ a₂ - a₁ ≠ a₃ - a₂

Since the difference between any two consecutive terms is not same

So the given sequence is not an arithmetic sequence.

Step 3 of 3 :

Identify the sequence is geometric or not

$\displaystyle \sf \frac{a_2 }{a_1} = \frac{0.8}{1.6} = \frac{1}{2} = 0.5$

$\displaystyle \sf \frac{a_3 }{a_2} = \frac{0.4}{0.8} = \frac{1}{2} = 0.5$

$\displaystyle \sf \therefore \: \frac{a_2 }{a_1} = \frac{a_3 }{a_2}$

Since the ratio between any two consecutive terms is same which is 0.5

So the given sequence is a geometric sequence

Hence , the sequence 1.6 , 0.8 , 0.4 , 0.2 is a geometric sequence

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