Question

Find the next number in the series:- 2, 6, 30, 210, _____

Answer 1

1890

2×3=6

6×5=30

30×7=210

210×9=1890

Answer 2

The next number in the series is 1890

Given : The given series is, 2,6,30,210...

To find : The next number in the series.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the next number in the series)

First of all, we have to figure out the mathematical relationship between two consecutive numbers of the given series.

If we analyse the numbers of the given series, one after another, we will get :

• First number = 2
• Second number = 6 = 2×3 = First number × 3
• Third number = 30 = 6 × 5 = Second number × (3+2) = Second number × [3 + {2 × (3-2)}]
• Fourth number = 210 = 30 × 7 = Third number × (3+4) = Third number × [3+ {2×(4-2)}]

By analysing the above mentioned mathematical series, we can say that :

nth number of the given series = (n-1)th number × [3 + {2× (n-2)}]

So, 5th number of the given series (i.e. n = 5) :

= (5-1)th number × [3+ {2 × (5-2)}]

= 4th number × (3+6)

= 210 × 9

= 1890

(This will be considered as the final result.)

Hence, the next number in the series is 1890