Question

Find the missing number.
$522,1235,2661,4800,7652,11217, ?$
A. $15495$
B. $16208$
C. $14782$
D. $16921$

Answer 1

Hint: The given problem is based on the sequence or series. A sequence or series is a numerical pattern and it is governed by a logical rule in which numbers in the sequence are called terms.
In the given question we will have to find the next term of the sequence. To find the next term of the sequence,
First we find the pattern of the sequence by applying different logical operations and when we find this pattern then we repeat the sequence. After that by using this pattern we get required next term of the given sequence.

Complete step by step solution:
The given problem is based on the sequence or series. A sequence or series is a numerical pattern and it is governed by a logical rule in which numbers in the sequence are called terms.
The given sequence are $522,1235,2661,4800,7652,11217$
We use a logical operation for getting the pattern of the sequence
In the given sequence for getting the second term we multiply $1$ by $713$ and add the result in the first number and similarly for getting third term we multiply $2$ by $713$ and add the result in the second term this process continue up to last term of the sequence.
$
  522 + 1 \times 713 = 522 + 713 = 1235 \\
  1235 + 2 \times 713 = 1235 + 1426 = 2661 \\
  2661 + 3 \times 713 = 2661 + 2139 = 4800 \\
  4800 + 4 \times 713 = 4800 + 2852 = 7652 \\
  7652 + 5 \times 713 = 7652 + 3565 = 11217 \\
 $
Now by using this pattern we find the next term of the sequence
$11217 + 6 \times 713 = 11217 + 4278 = 15495$
Therefore the next required number of sequences is $15495$.

So, the correct answer is “Option A”.

Note: A sequence that continues indefinitely without terminating is an infinite sequence, whereas a sequence with an end is known as a finite sequence.
There are different types of questions based on the sequence that can be asked. For example: to find the next term in the given sequence, identify a term that is wrongly placed in a given sequence, find the missing term in a certain sequence and complete a given sequence. To solve this all types of questions first we will have to identify the pattern of the sequence. Then by using this pattern we can get the required answer.