In the series below, numbers and letters come by turns, and the numbers and the letters each follow their own repeating pattern.
3 B 6 D 3 F 6 B 3 D 6 F 3 B 6 D
If the series is continued in the same way, what will be the 39th and the 40th terms?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6, D
Split the series into the numbers (odd places) and the letters (even places); find the place of each wanted term inside its own series.
Numbers: 3 6 3 6 ...; the repeating group is 3 6 (2 terms)
Letters: B D F B D F ...; the repeating group is B D F (3 terms)
The 39th term is in an odd place, so it is the \((39+1)\div2=20\)th number; 20 is even, so it is the 2nd of 3 6, that is 6
The 40th term is in an even place, so it is the \(40\div2=20\)th letter; \(20\div3\) leaves remainder 2, so it is the 2nd of B D F, that is D