Question

Find the next number in the series 4, 12, 30, 68, ……….
A. 140
B. 146
C. 160
D. 144

Answer 1

Hint: If we observe the given series, then we can observe that this series has a special pattern. Each of the consecutive terms is formed by the general form, $\left( n\times 2 \right)+2\left( x \right)$, where n is the preceding term and x is the position of the term. Like, we have 4 as the first term and 12 as the second term. So, 12 can be expressed as, $\left( 4\times 2 \right)+\left( 2\times 2 \right)=8+4=12$.

Complete step-by-step answer:
We have been given a series in the question, that is, 4, 12, 30, 68, ………. And have been asked to find the next number in the series. Let us assume the next number in the series as X. Now, if we observe this given series, then we can make out that there is a special pattern in it. We can see that each of the consecutive terms are formed by the general pattern of $\left( n\times 2 \right)+2\left( x \right)$, where, n is the preceding term and x is the position of the term. If we take the first term of the series, 4, the we can represent it in that form as follows,
$\left( 4\times 2 \right)+\left( 2\times 2 \right)=8+4=12$
Similarly, we can represent the next term of the series, 30 as follows,
$\left( 12\times 2 \right)+\left( 2\times 3 \right)=24+6=30$
Now, we can represent the next given term, 68 as,
$\left( 30\times 2 \right)+\left( 2\times 4 \right)=60+8=68$
So, the next term X can be represented as,
$\left( 68\times 2 \right)+\left( 2\times 5 \right)=136+10=146$
Therefore, the next term in the given series is 146.
Hence, option B is the correct answer.

Note: Most of the time the students try to find the common difference and then check if it is in GP or HP. But it is not necessary that all series are part of any of these three types of series. As a result, many students skip such questions in the exams. Therefore, it is advisable to think of a general pattern for the series in such types of questions.