Question

Complete the following series: $90,180,12,50,100,200,?,3,50,4,25,2,6,30,3.$

Answer 1

Find the missing term of the series by observing the pattern :

In Given series,$90,180,12,50,100,200,?,3,50,4,25,2,6,30,3.$

Notice that the first term $\text{'}90\text{'}$ of the series is the product of the last term $\text{'}3\text{'}$ and the second last term $\text{'}30\text{'}$ of the series.

$90=30\times 3$

Again, the second term $\text{'}180\text{'}$ of the series is the product of the second last $\text{'}30\text{'}$ and third last term $\text{'}6\text{'}$ of the series.

Similarly,

$\begin{array}{l}12=6\times 2\\ 50=2\times 25\\ 100=25\times 4\\ 200=4\times 50\end{array}$

Hence the missing number must be the product $50$ and $3$

Find the missing term:

$50\times 3=150$

Hence, the missing number is $150$.

Hence the complete series is $90,180,12,50,100,200,150,3,50,4,25,2,6,30,3.$