The sequences that are arithmetic are
A. 4, 14, 24, 34, …
B. 9, 5, 1, −3, …
and C. 1.1, 1.2, 1.3, 1.4, …
An arithmetic sequence is one in which the difference between one term and the next is a constant, that is, there is common difference between consecutive terms.
To determine which of the given sequences are arithmetic, we will check if there is a constant common difference between consecutive terms.
Let Tₙ represent the nth term; that is T₁ , T₂ , T₃ , ... represent the first, second, third terms and so on respectively.
Here, T₁ = 4, T₂ = 14, T₃ = 24, T₄ = 34, ...
The difference between the first and second terms is
T₂ - T₁ = 14 - 4 = 10
The difference between the second and third terms is
T₃ - T₂ = 24 - 14 = 10
The difference between the third and fourth terms is
T₄ - T₃ = 34 - 24 = 10
Since the common difference (10) between the consecutive terms is constant, it is arithmetic.
Here, T₁ = 9, T₂ = 5, T₃ = 1, T₄ = -3, ...
The difference between the first and second terms is
T₂ - T₁ = 5 - 9 = - 4
The difference between the second and third terms is
T₃ - T₂ = 1 - 5 = - 4
The difference between the third and fourth terms is
T₄ - T₃ = -3 - 1 = - 4
Since the common difference (- 4) between the consecutive terms is constant, it is arithmetic.
Here, T₁ = 1.1, T₂ = 1.2, T₃ = 1.3, T₄ = 1.4, ...
The difference between the first and second terms is
T₂ - T₁ = 1.2 - 1.1 = 0.1
The difference between the second and third terms is
T₃ - T₂ = 1.3 - 1.2 = 0.1
The difference between the third and fourth terms is
T₄ - T₃ = 1.4 - 1.3 = 0.1
Since the common difference (0.1) between the consecutive terms is constant, it is arithmetic
Here, T₁ = 1, T₂ = 2, T₃ = 4, T₄ = 8, ...
The difference between the first and second terms is
T₂ - T₁ = 2 - 1 = 1
The difference between the second and third terms is
T₃ - T₂ = 4 - 2 = 2
The difference between the third and fourth terms is
T₄ - T₃ = 8 - 4 = 4
Since the common difference between consecutive terms is NOT constant, it is not arithmetic.
Hence, the sequences that are arithmetic are
A. 4, 14, 24, 34, …
B. 9, 5, 1, −3, …
and C. 1.1, 1.2, 1.3, 1.4, …
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