Question

What number comes next in the sequence below ?
$3624$ , $4363$ , $3644$ , $4563$ , $3664$ ,______
$\left( A \right){\text{ }}4763$
$\left( B \right){\text{ 3}}763$
$\left( C \right){\text{ 3}}624$
$\left( D \right){\text{ }}6763$

Answer 1

In this question, we need to solve that incomplete numerical sequence in the same pattern in which the complete numerical sequence is given. There are two alternating series present in the sequence so we have to find the next term accordingly. Observing the series, which type of series it is, will help us to find the next number of the sequence.

Complete step by step answer:
A sequence is a set of things( usually numbers) that are in order. Each number in the sequence is known as ‘term’ or ‘element’ or ‘member’.
An arithmetic series is the sum of a sequence $\left( {{a_k}} \right)$ where k $= 1,2,3,....$ in which each term is computed from the previous one by adding or subtracting a constant d. Therefore, for $k > 1$ ,
${a_k} = {a_{k - 1}} + d = {a_{k - 2}} + 2d = ....... = {a_1} + d(k - 1)$
The sequence given to us is $3624$ , $4363$ , $3644$ , $4563$ , $3664$ ,______ . By observing this sequence carefully we find that there are two alternating series present in this sequence. And both alternating series are the arithmetic series.
The first is even terms of sequence : $3624$ , $3644$ , $3664$ ,………..
In this series there is a difference of $20$ between each term of the series. That is this series is obtained by adding $20$ to the previous number as shown below:
$3624 + 20 = 3644$ ,
$3644 + 20 = 3664$ ,
And $3664 + 20 = 3684$
Also the second is odd terms of sequence: $4363$ , $4563$ ,………
In this series there is a difference of $200$ between each term of the series. That is this series is obtained by adding $200$ to the previous number as shown below:
$4363 + 200 = 4563$ ,
And $4563 + 200 = 4763$
As we need to find the term which comes after the term $3664$ . And we also know that there are two alternating series. So that means the term comes after $3664$ should be of the second series. Therefore, $4763$ is the number that comes next in the sequence $3624$ , $4363$ , $3644$ , $4563$ , $3664$ ,______ .
Hence, the correct option is $\left( A \right){\text{ }}4763$.

Note:
Note that a number series is just a sequence of numbers arranged in some logical way. Remember that we need to identify the pattern and answer the missing number. Keep in mind that before answering the question you have to check the pattern of the question. Once a constant difference is achieved you are able to find the next number of the sequence.