Question

Look at this series: $36,34,30,28,24$
What number should come next in the series?

Answer 1

Hint: The given question requires us to find the next term in the sequence provided to us. We have to find out whether the given series or sequence is an arithmetic progression, a geometric progression, a harmonic progression, an arithmetic geometric progression or some other special type of series. Hence, we first have to generalize a formula for the terms of the given sequence.

Complete step-by-step solution:
The given problem puts our analytical skills to test. We have to first identify the nature of the given sequence or series and then find a generalized formula for the terms of the sequence.
The sequence given to us is: $36,34,30,28,24$.
First checking the given series for arithmetic progression.
The difference between the first two terms of the sequence is $34 - 36 = - 2$.
The difference between the second and the third term of the sequence is $30 - 34 = - 4$.
Difference between the third and the fourth term of the sequence is $28 - 30 = - 2$.
Similarly, the difference between the forth and the fifth term of the sequence is $24 - 28 = - 4$.
Since the difference between the consecutive terms of the series is not equal, hence it is not an arithmetic progression.
But, on observing carefully, we can see that the difference between the alternate pairs of two terms is equal. This means that the difference between first and second term is equal to difference between third and fourth terms and so on.
So, we can say that the difference between two consecutive terms alternately switches between $ - 4$ and $ - 2$.
Now, we know that the difference between the last two terms of the series, $24$ and $28$ is $ - 4$. So, the difference between the upcoming term and $24$ should be $ - 2$.
Let the next term in series be x.
So, we have, $x - 24 = - 2$
Shifting the terms in the equation, we get,
$ \Rightarrow x = - 2 + 24$
Carrying out the calculations, we get,
$ \Rightarrow x = 22$
So, the value of x is $22$. Hence, the next number in series is $22$.
Therefore, option (B) is the correct answer.

Note: In such a type of question, we should first find out the nature of the series and then try to figure out the general term of the series. In this way, we would have an idea beforehand of what the formula for the general term of the sequence would look like. Care should be taken while observing the pattern of the series as it may lead to an incorrect answer.