Step by step
The question
Question: The pattern A, B, C, D, A, B, C, D, ...
keeps repeating.
What is the 30th letter?
1 Find the block
The list starts again after D.
So the block that repeats is A, B, C, D.
block = A, B, C, D
The block is 4 long.
length = 4
2 Divide
The block comes again and again.
So we divide by its length.
What is left over tells us the place in the block.
n ÷ (length of the block): what is left = the place in the block
4 times 7 is 28.
So 7 full blocks take us to the 28th letter.
30 minus 28 is 2 more.
30 ÷ 4 = 4 × 7 = 28, 30 − 28 = 2
3 Count into the block
Careful!
The 7 only counts full blocks.
The 2 left over gives the place.
Careful: not 7: the number of blocks ✗
2 left means place 2 in the block: B.
30th letter = place 2 in the block = B
4 Check
Let's check by counting on.
A block ends at the 28th letter.
Then we count on: A, B.
The 30th is B.
So it is right!
28th = D (end of a block), 29th = A, 30th = B ✓
Let's look back.
First: find the block.
Then: divide.
Then: count into the block.
Last: check.
Answer
30th letter = place 2 in the block = B