Question

find the value of x

5,7,10,15,23,x

Answer 1

ANSWER:

Given:

• 5, 7, 10, 15, 23, x

To Find:

• Value of x

Solution:

We are given a series,

⇒ 5, 7, 10, 15, 23, x

To find the value of x, we need to find the pattern the series has.

So, we will try the most common pattern, i.e., difference of consecutive terms, and see if there exists a pattern.

So, difference of consecutive terms,

• ⇒ 5, 7 = 7 - 5 = 2
• ⇒ 7, 10 = 10 - 7 = 3
• ⇒ 10, 15 = 15 - 10 = 5
• ⇒ 15, 23 = 23 - 15 = 8
• ⇒ 23, x = x - 23

So, the differences are: 2, 3, 5, 8, x - 23

Now, taking difference of consecutive terms of the above mentioned series of differences,

• ⇒ 2, 3 = 3 - 2 = 1
• ⇒ 3, 5 = 5 - 3 = 2
• ⇒ 5, 8 = 8 - 5 = 3
• ⇒ 8, x - 23 = x - 23 - 8 = x - 31

So, the differences of differences are: 1, 2, 3, x - 31

We can see that the difference are consecutive terms

So, after 3, the difference of differences is 4.

Hence,

⇒ 4 = x - 31

⇒ x = 31 + 4

⇒ x = 35

Therefore, the value of x is 35.