Question

Find out whether the sequence 3, 3, 3, 3, …… is an AP if it is find out the common difference from the following options:
A. Yes, d=0
B. No
C. Yes, d=3
D. Yes, d=1

Answer 1

Hint:In order to solve this problem you need to first check if it is an AP then you will automatically get the common difference d. Proceeding like this will give you the right answer.

Complete step-by-step answer:
 The given AP is 3, 3, 3, 3……
We see from the AP that the first, second, third and fourth term are:
$
  {a_1} = 3 \\
  {a_2} = 3 \\
  {a_3} = 3 \\
  {a_4} = 3 \\
$
We can find the common difference as:
${a_2} - {a_1} = {d_1}$
3 – 3 = 0
${a_3} - {a_2} = {d_2}$
3 – 3 = 0
${a_4} - {a_3} = {d_3}$
3 – 3 = 0
We see that the difference between the terms is the same therefore it is an AP with common difference 0.
The correct option is A.

Note: Whenever you face such type of problems you need to know that if a series is given then by subtracting the consecutive term if we get the difference same then it is an AP with that common difference. Proceeding like this will give you the right answer.