Question

Which number will continue the same pattern in the given series and how?

26, 312, 420, 530, 642, __​

Answer 1

ANSWER:

Given:

• Series : 26, 312, 420, 530, 642, __

To Find:

• Next number in the series.

Solution:

Let the next number be x.

We are given, the series,

⇒ 26, 312, 420, 530, 642, x

Now, if we observe the series, we can make out the following pattern,

⇒ 26, 312, 420, 530, 642

⇒ (2)(6), (3)(12), (4)(20), (5)(30), (6)(42)

Now, the numbers written in the first brackets of each term form one series and the numbers written in the second brackets of each term form other series.

That is,

⇒ Serie 1 = 2, 3, 4, 5, 6

And,

⇒ Serie 2 = 6, 12, 20, 30, 42

For the next term in the given series, we will find the next terms in the above mentioned sub-series and join them.

So, taking Serie 1 first.

⇒ Serie 1 = 2, 3, 4, 5, 6, a

We can see that the terms in this serie are consecutive numbers starting from 2.

So, the next term(a) will be 7.

Now, we'll take Serie 2.

⇒ Serie 2 = 6, 12, 20, 30, 42, b

Taking difference of consecutive terms,

⇒ 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10, 42 - 30 = 12.

Taking the differences,

⇒ 6, 8, 10, 12

We can see that, the differnces form a serie of even numbers starting from 6.

So, using this pattern, the next difference should be 14.

That means,

⇒ b - 42 = 14

⇒ b = 56

The next term(b) in Serie 2 is 56.

Now, we know that, x will be formed by joining a and b. That is,

⇒ x = (a)(b)

Hence,

⇒ x = (7)(56)

⇒ x = 756

Therefore, next term in the series is 756.