# Q. What is the value of X in the sequence 2, 12, 36, 80, 150, X?

a. 248

b. 252

c. 258

d. 262

Correct Answer: b. 252

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

2, 12, 36, 80, 150, X

Consider the differences between consecutive terms:

12 – 2 = 10

36 – 12 = 24

80 – 36 = 44

150 – 80 = 70

Now let’s examine the differences between these differences:

24 – 10 = 14

44 – 24 = 20

70 – 44 = 26

We see that the differences between the differences are increasing by 6 each time. Therefore, to find the next difference between consecutive terms, we can add 6 to the last difference between differences:

26 + 6 = 32

Now we can add this difference to the last difference between consecutive terms in the original sequence:

70 + 32 = 102

Finally, to find the value of X, we can add this difference to the last term in the original sequence:

150 + 102 = 252

Thus, the value of X is 252 (option b).