Question

3, 5, 7, 9, 11, 13, 15 is an
A) Geometric Progression
B) Arithmetic series
C) Arithmetic progression
D) Harmonic progression

Answer 1

Hint:
Successive terms are obtained by adding a fixed number to the proceeding term.
such a list of numbers is said to form an Arithmetic Progression (AP) so an Arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the proceeding term Except for the first term.
This fixed number is called the common difference of the AP.

Complete step by step solution:
Step1:
Given 3,5,7,9, 11, 13,15
Here the first term is 3 which is denoted by are so ${a_3}$.
The second term is 5 which is denoted by \[{a_2}\] So
The third term is 7, which is denoted by \[{a_4} - {a_3} = 9 - 7 = 2\] And so on…
step2:
If 1st term \[{a_1}\] is subtracted from the Second-hand term \[{a_2}\]
we get to the value is \[{a_2}\]-\[{a_1}\] = 5-3=2.
Similarly, if the second term (\[{a_2}\]) is subtracted from the third term (\[{a_3}\]),
we get the value \[{a_4} - {a_3} = 9 - 7 = 2\] and so on in the Given term,
Each term is more than the term preceding it. So this is an arithmetic progression.
So this is an arithmetic progression.

Hence option c is correct.

Note:
1) a, a+d, a+2d,a+3d……represent an Arithmetic progression where the first term and d is a common difference. This is called the General form of an arithmetic progression.
2) Remember that it can be positive, negative, or zero.
3) Let us denote the first term of An AP by a second term by\[a - {a_3}{a_3} - {a_2} = ........{a_n} - {a_{n - 1}}\] ${a_2}..............{n_{th}}$ term by ${a_n}$and the common difference by d
Then the AP becomes as ${a_{_1}}{a_2}{a_3}........{a_n}$So ${a_{_2}} - {a_{1 = }}{a_3} - {a_2} = ........{a_n} - {a_{n - 1}}$= d