Question

A sequence is also called as
A.Arithmetic series
B.Progression
C.Geometric Series
D.None

Answer 1

Hint: Here, we will follow the concepts of all the terms given that are arithmetic series, geometric series, sequence and progression one by one. Then we will observe what sequence is also known as.

Complete step-by-step answer:
An Arithmetic Progression (AP) is the sequence of numbers in which the difference of two successive numbers is always constant.
The standard formula for Arithmetic Progression is – $ {a_n} = a + (n - 1)d $
Where $ {a_n} = $ nth term in the AP
 $ a = $ First term of AP
 $ d = $ Common difference in the series
 $ n = $ Number of terms in the AP
Whereas, the geometric progression (G.P.) is the sequence in which succeeding element is obtained by multiplying the preceding number by the constant and the same continues for the series. The ratio between the two remains the same.
The standard formula for geometric progression is –
 $ {T_n} = a.{r^{n - 1}} $
Where, $ a = $ first term
 $ r = $ Common ratio of the finite G.P with “n” terms.
Sequence can be expressed as the set of numbers which are arranged in according to any specific rule, where there is no exception for any type of numbers or any type of rules according to which they are arranged. But the thing is there should be the set of numbers with the definite, logical rule according to which they are arranged.
For Example, $ 2,3,5,7,13,17,.... $ is the sequence which follows the logic of being prime numbers.
Also, progression is the set of numbers which are arranged according to specific and definite rules.
Hence, sequence is also called as the progression.
So, the correct answer is “Option B”.

Note: Know the difference between the arithmetic and geometric progression and apply the concepts accordingly. In arithmetic progression, the difference between the numbers is constant in the series whereas the geometric progression is the sequence in which the succeeding element is obtained by multiplying the preceding number by the constant and the same continues for the series. The ratio between the two remains the same.