# Q. What is the sum of the first 28 terms in the following sequence?

1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, ..

a) 83

b) 84

c) 85

d) 86

Correct answer: b) 84

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

**Explanation:**

## Sum of first 28 terms

Let’s approach this step-by-step:

1) First, let’s identify the pattern in this sequence. It appears to be:

– Count up from 1 to n

– Then count back down to 1

– Repeat with n increasing by 1 each time

2) Let’s write out the first 28 terms:

1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2

3) Now, let’s sum these numbers:

1 + 1 + 2 + 1 + 3 + 2 + 1 + 4 + 3 + 2 + 1 + 5 + 4 + 3 + 2 + 1 + 6 + 5 + 4 + 3 + 2 + 1 + 7 + 6 + 5 + 4 + 3 + 2

Calculating this sum: The sum is 84