Question

6,9,13,21,38,71,? find the missing number​

Answer 1

ANSWER:

Given:

• 6, 9, 13, 21, 38, 71,

To Find:

• Next term in series

Solution:

Let the next term in the series be x.

So, the series becomes,

⇒ 6, 9, 13, 21, 38, 71, x

Now, we will take the easiest approach of solving series’ question that is of difference between consecutive terms and observe if they form a certain pattern.

So,

⇒ Differences of given terms:

• 9 - 6 = 3
• 13 - 9 = 4
• 21 - 13 = 8
• 38 - 21 = 17
• 71 - 38 = 33
• x - 71 = x - 71

Let’s write all the differences as a separate series:

⇒ 3, 4, 8, 17, 33, (x - 71)

We can see, that this doesn’t form a specific pattern. Let’s take the difference of these terms, and observe them.

So,

⇒ Differences of given terms:

• 4 - 3 = 1
• 8 - 4 = 4
• 17 - 8 = 9
• 33 - 17 = 16
• x - 71 - 33 = x - 104

Let’s write all the differences as a separate series:

⇒ 1, 4, 9, 16, (x - 104)

We can rewrite the following terms as

⇒ 1², 2², 3², 4², (x - 104)

So, here we get a pattern. The above series has squares of consecutive numbers.

So, by same logic the next term will be:

⇒ 5²

But, next term is (x - 104).

Hence,

⇒ x - 104 = 5²

⇒ x - 104 = 25

⇒ x = 104 + 25

⇒ x = 129

Therefore, the next term of the series mentioned in question is 129.