Question

A sequence is given as \[3,5,7,9,11,13,15,\] . . . . . . . . . . . . . . . . . which is an
A. Geometric Progression
B. Arithmetic series
C. Arithmetic Progression
D. Harmonic Progression

Answer 1

Hint: Given sequence is \[3,5,7,9,11,13,15,\] . . . . . . . . . . . .
For the given sequence we can easily say that the two consecutive terms have the same difference that means the common difference is 2, writing all the other terms can say which type of progression it follows.

Complete step-by-step solution -
Arithmetic Progression: An arithmetic progression is a list of numbers in which each term is obtained by term adding a fixed number ‘d’ to preceding term, except the first term.
a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d . . . . . . . . . . . . . . . . . . .(a)
Given sequence is \[3,5,7,9,11,13,15,\] . . . . . . . . . . . .
Here common difference is \[5-3=7-5=9-7=2\]
In the given sequence \[3,5,7,9,11,13,15,\] . . . . . . . . . . . . . . . . . . . .
The first term a is 3 and common difference d is 2.
Substituting the values of a and d in (a) we get,
\[3,3+2,3+2\left( 2 \right),3+2\left( 3 \right),\]. . . . . . . . . . . .
Which is the given sequence.
Therefore the above sequence is an arithmetic progression.

Note: Finding the common difference is the key step in this type of problem. From that writing all the terms in a certain sequence gives the progression. Care should be taken while writing the terms. Mistake in one step leads to the change in solution.