Question

Find the type of series $3, 5, 7, 9, 11, 13, 15....$
$\left( a \right){\text{ Geometric progression}}$
$\left( b \right){\text{ Arithmetic series}}$
$\left( c \right){\text{ Arithmetic progression}}$
$\left( d \right){\text{ Harmonic progression}}$

Answer 1

This question can be easily solved by seeing the sequence but the important thing is what we say to this type of sequence. Here the common difference between the two consecutive terms is constant which is $2$. So now we can easily answer which type of progression this belongs to.

Complete step by step solution:
As we know that the sequence in which the difference between any two consecutive terms is a constant then we called it arithmetic progression.
So here in this question, we see that the difference between the two sequences is $2$, so we can say that this sequence belongs to arithmetic progression.
Therefore, the above sequence is an arithmetic progression.

Hence, the option $\left( c \right)$ is correct.

Additional information:
Geometric Progression is a series that is multiplied by a constant number repeatedly. A geometric progression, otherwise called a geometric succession, is an arrangement of numbers where each term after the first is found by increasing the past one by a fixed, non-zero number called the regular proportion.
A harmonic progression is a succession of genuine numbers framed by taking the reciprocals of a math movement. Identically, it is a succession of genuine numbers with the end goal that any term in the grouping is the consonant mean of its two neighbors.
An arithmetic sequence grouping is a progression of numbers where each number differentiates from the past number and the accompanying number by a regular qualification. For instance, in the number-crunching grouping $1, 3, 5, 7, 9$, this regular distinction is $2$ without fail.
An arithmetic series is the grouping of the nth incomplete amounts of the first number-crunching successions. Fundamentally, it's adding the first, second, third… and nth terms of the arrangements together. For instance, the number-crunching arrangement related to the $1, 3, 5, 7, 9$ succession

Note:
The main thing in this type of question is if we know the sequence or we can say if we understand the sequence series then we can easily answer this also we can solve it easily by using the formula associated with the progression.