Question

Look at the series: \[2,6,18,54,...\] What number should come next?
a). \[108\]
b). \[148\]
c). \[162\]
d). \[216\]

Answer 1

Hint: As we see that it is a number series we need to first find the type of series, we observe the first and second terms of the series and notice that the series is a multiplication series. So, we try to analyze the relationship between the first term and the second term.

Complete step-by-step solution:
We observe that the given series is a multiplicative series.
We take the first term that is \[2\] and the second term \[6\], we notice here that the second term in the series is \[3\]multiplied by the first term. And similarly, the third term \[18\] is \[3\] multiplied by the second term\[6\].
That is, the whole series has numbers \[3\]times more than the previous number.
Rule\[ = (1st\]number\[ \times \] \[3\]\[ = 2nd\]number), (\[2nd\]number\[ \times \] \[3\]\[ = 3rd\]number) and so on.
Therefore, the next number after \[54\] is equal to \[54 \times 3 = 162\]
Hence, the correct option is (c)\[162\].
Additional information: Number series is an imроrtаnt tорiс found in mаths. Number series аre оf different tyрes рerfeсt сube series, Geоmetriс series, Аrithmetiс series, Twо stаge series, Mixed series, Аrithmetiсо- Geоmetriсо series, Аlternаte series etс. Series is sequentiаl оrder оf letters, numbers or both arranged in such а wау thаt eасh term in the series is obtained ассоrding tо sоme sрeсifiс rules. These rules саn be bаsed оn mаthemаtiсаl орerаtiоns, рlасe оf letters in аlрhаbetiсаl оrder оr sо оn. In questiоns relаted tо number series а sрeсified sequence or оrder оf letters, numbers or combination оf аll.

Note: It is useful to find the type of series that is given. We must analyze each term of the series and then find its pattern and then find the next number of the series. The pattern that we draw between our first and second term tells us a general representation of the pattern of the whole series.