# Q. What will come in place of * in the sequence 3, 14, 39, 84, *, 258?

a) 150

b) 155

c) 160

d)176

Correct answer: b) 155

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

The sequence follows a specific pattern based on the hint provided. Each number in the sequence is the sum of a number (n), its square (n²), and its cube (n³), where n starts at 1 and increases by 1 for each term.

Let’s break down each term in the sequence:

1. 3 = 1 + 1² + 1³ = 1 + 1 + 1 = 3

2. 14 = 2 + 2² + 2³ = 2 + 4 + 8 = 14

3. 39 = 3 + 3² + 3³ = 3 + 9 + 27 = 39

4. 84 = 4 + 4² + 4³ = 4 + 16 + 64 = 84

5. * (the missing term) = 5 + 5² + 5³ = 5 + 25 + 125 = 155

6. 258 = 6 + 6² + 6³ = 6 + 36 + 216 = 258

As we can see, the missing term (*) corresponds to n = 5 in the pattern.

Therefore, the number that should replace * in the sequence is 155, which matches option b) in the given choices.