Question

Identify the pattern and write the next number.
11, 27, 43, 59, ?
${\text{A}}{\text{. 74}} \\
  {\text{B}}{\text{. 73}} \\
  {\text{C}}{\text{. 76}} \\
  {\text{D}}{\text{. 75}} \\ $

Answer 1

Hint: Here we have given four terms of a pattern and we have to find a fifth term. Here if we notice a pattern is AP because the difference of two consecutive terms is the same and that same difference is called a common difference in AP. So for the next number in this pattern we have to add this common difference in the fourth term so that we can get a fifth term.

Complete step-by-step answer:
We have given
$11 , 27 , 43 , 59 $
Here we can notice
$27 – 11 = 16$
$43 – 27 =16$
$59 – 43 = 16$
So we can see the difference of any consecutive term is constant so this pattern is AP and its common difference is 16.
So if we have to find the next term of this pattern then we just have to add the common difference in the last term given.
We have
Last term = $59$
Common difference = $16 $
Next term will be = $59+16 = 75 $
Hence option D is the correct option.

Note: Whenever we get this type of question the key concept of solving is we have to understand the pattern and then we have to just follow the pattern to solve this type of question. Here AP is the pattern so we have to understand AP ( An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence $1, 2, 3, 4,...…$ is an arithmetic progression with common difference 1.)