Engineering Board Exam Reviewer · Sequences and Series · hard
The increasing sequence 1, 3, 4, 9, 10, 12, 13, consists of all positive integers which are powers of 3 or sums of distinct powers of 3. Find the 100th term of this sequence.
- 832
- 455
- 981
- 1090
Answer
C. 981
Solution
Rewriting each term index in base 3 (analogous to writing 1..n in binary for powers of 2) shows the 100th term corresponds to base-3 digits 1100100, i.e., 36+35+32 = 981.
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