Question

Which sequences are arithmetic? Select three options. -8. 6, –5. 0, –1. 4, 2. 2, 5. 8, … 2, –2. 2, 2. 42, –2. 662, 2. 9282, … 5, 1, –3, –7, –11, … –3, 3, 9, 15, 21, … –6. 2, –3. 1, –1. 55, –0. 775, –0. 3875, ….

Answer 1

To solve the problem we must know about Arithmetic Sequence.

Arithmetic Sequence

An arithmetic sequence is a sequence in which the difference between any two terms of the sequence is the same or equal.

$a_n = a_1 + (n-1)r$

where,

$a_n$ is the nth term of the sequence,

$a_1$ is the first term of the sequence,

r is a common difference between every two terms.

The options that are arithmetic sequences are A, C, and D.

Explanation

Given options

A.)   -8. 6, –5. 0, –1. 4, 2. 2, 5. 8, …

B.)   2, –2. 2, 2. 42, –2. 662, 2. 9282, …

C.)   5, 1, –3, –7, –11, …

D.)   –3, 3, 9, 15, 21, …

E.)   –6. 2, –3. 1, –1. 55, –0. 775, –0. 3875, ….

A.)   -8. 6, –5. 0, –1. 4, 2. 2, 5. 8, …

$a_1 = -8.6\\ a_2 = -5.0\\ a_3 = -1.4\\ a_4 = 2.2\\ a_5 = 5.8$

We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.

$a_1 - a_2= -8.6 - (-5.0) = -3.6\\ a_2 -a_3= -5.0 - (-1.4)= -3.6\\ a_3 -a_4= -1.4-2.2 = -3.6$

Hence, the series is an arithmetic Sequence.

B.)   2, –2. 2, 2. 42, –2. 662, 2. 9282, …

$a_1 = 2\\ a_2 = -2.2\\ a_3 = 2.42\\ a_4 = -2.662\\ a_5 = 2.9282$

We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.

$a_1 - a_2= 2- (-2.2) = 4.2\\ a_2 -a_3= -2.2- (2.42)= 0.22$

Hence, the series is not an arithmetic Sequence.

C.)   5, 1, –3, –7, –11, …

$a_1 = 5\\ a_2 = 1\\ a_3 = -3\\ a_4 = -7\\ a_5 = -11$

We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.

$a_1 - a_2= -4\\ a_2 -a_3= -4\\ a_3 -a_4= -4$

Hence, the series is an arithmetic Sequence.

D.)   –3, 3, 9, 15, 21, …

$a_1 = -3\\ a_2 = 3\\ a_3 = 9\\ a_4 = 15\\ a_5 = 21$

We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.

$a_1 - a_2= 6\\ a_2 -a_3= 6\\ a_3 -a_4= 6$

Hence, the series is an arithmetic Sequence.

E.)   –6. 2, –3. 1, –1. 55, –0. 775, –0. 3875, ….

$a_1 = -6.2\\ a_2 = -3.1\\ a_3 = -1.55\\ a_4 = -0.775\\ a_5 = -0.3875$

We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.

$a_1 - a_2= -6.2- (-3.1) = -3.1\\ a_2 -a_3= -3.1- (-1.55)= -1.55$

Hence, the series is not an arithmetic Sequence.

Hence, the options that are arithmetic sequences are A, C, and D.

Learn more about Arithmetic Sequence:

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