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,……

1. A. 83
2. B. 84
3. C. 85
4. D. 86

Answer: B

Explanation

The sequence can be broken down into blocks, where the k-th block consists of numbers from 1 up to k, preceded by a 1, and the block itself sums to k(k+1)/2:
– Block 1: (1) – 1 term, sum = 1
– Block 2: (1, 2) – 2 terms, sum = 3
– Block 3: (1, 3, 2) – 3 terms, sum = 6
– Block 4: (1, 4, 3, 2) – 4 terms, sum = 10
– Block 5: (1, 5, 4, 3, 2) – 5 terms, sum = 15
– Block 6: (1, 6, 5, 4, 3, 2) – 6 terms, sum = 21
– Block 7: (1, 7, 6, 5, 4, 3, 2) – 7 terms, sum = 28

Let’s count the total number of terms up to Block 7: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 terms.
So, the first 28 terms are exactly these 7 blocks. The sum of these 28 terms is the sum of the sums of these blocks:
Total Sum = 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84. This question tests pattern recognition and summation of series, a common topic in CSAT.