Question

Find the next number of the series:(ਦਿੱਤੀ ਲੜੀ ਦਾ ਅਗਲਾ ਅੰਕ ਪਤਾ ਕਰੋ): 12,13,14,18,26,35, ? *

52

62

46

44

​

Answer 1

Question :

›»› Find the next number of the series 12,13,14,18,26,35, ?

(A) 52

(B) 62

(C) 46

(D) 44

Answer :

›»› The next number of the series 12, 13, 14, 18, 26, 35 is 62.

Given :

• The series 12, 13, 14, 18, 26, 35.

To Find :

• The next number of the series.

Solution :

To find the next number of the series we add 1², 1³, 2², 2³, 3², 3³ with the series.

Since, we are provided with the series 12, 13, 14, 18, 26, 35, we can use the logic :

1², 1³, 2², 2³, 3², 3³ to find to next number of the series.

→ 12 + 1²

→ 12 + 1

→ 13

→ 13 + 1³

→ 13 + 1

→ 14

→ 14 + 2²

→ 14 + 4

→ 18

→ 18 + 2³

→ 18 + 8

→ 26

→ 26 + 3²

→ 26 + 9

→ 35

→ 35 + 3³

→ 35 + 27

→ 62

Hence, the next number of the series 12, 13, 14, 18, 26, 35 is 62.

Option (B) 62 is correct ✔

Similarly, we can also find the other next numbers of the series, by adding 1², 1³, 2², 2³, 3², 3³, 4², 4³, 5², 5³ with the series.

Let's also find the other next numbers of the series.

→ 62 + 4²

→ 62 + 16

→ 78

→ 78 + 4³

→ 78 + 64

→ 142

→ 142 + 5²

→ 142 + 25

→ 167

→ 167 + 5³

→ 167 + 125

→ 292

Hence, the number of the series is 12, 13, 14, 18, 26, 35, 62, 78, 142, 167, 292...

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

• A series 12,13,14,18,26,35,?

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• The next number of the series

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

In these type of questions we need to find a relation among each element in the series.

$\:\:$

Let the unknown next number be "x"

$\:\:$

Let us have a look on the differences between pairs.

$\:\:$

• 13 - 12 = 1

• 14 - 13 = 1

• 18 - 14 = 4

• 26 - 18 = 8

• 35 - 26 = 9

$\:\:$

We can clearly observe some relation above , let me elaborate it.

$\:\:$

The above differences can also be written as:

$\:\:$

• 13 - 12 = 1 = $\rm 1 ^2$

• 14 - 13 = 1 = $\rm 1^3$

• 18 - 14 = 4 = $\rm 2^2$

• 26 - 18 = 8 = $\rm 2^3$

• 35 - 26 = 9 = $\rm 3^2$

$\:\:$

Now what will be the next difference , can we guess , wouldn't it be $\sf 3^3$

$\:\:$

So , We can say that ,

$\:\:$

$\sf \dashrightarrow x - 35 = 3^3$

$\:\:$

Or,

$\:\:$

$\sf \longmapsto x = 3^3 + 35$

$\:\:$

$\sf \longmapsto x = 27 + 35$

$\:\:$

$\purple\longrightarrow$ $\bf x = 62$

$\:\:$

• Hence , Option 2) i.e 62 is the correct answer

$\:\:$

$\underline{\bold{\texttt{Conclusion}}}$

$\:\:$

The next number in the series is "62"

$\:\:$

So the series will be -

$\:\:$

• 12, 13, 14, 18, 26, 35, 62

$\rule{200}5$