Series (Number & Letter)
🔒 Log in to trackRepeating letter series — fill the blanks
🔒 Log in to trackA line of small letters has blanks, like a _ c a b _ a b c _ b c. The line follows one repeating pattern. Find the pattern, fill the blanks from left to right, and match the option. The pattern is a fixed block, a growing block, a mirror block or a rotating block.
What the question looks like
You see a line of small letters with some blanks. The options are groups like bca, bac, cab. Fill the blanks from left to right so the whole line repeats one pattern.
Think of a rangoli border. One small design repeats again and again. Once you know one design, you can fill any gap.
Step 1: find the block
Count all places, letters and blanks together. A line of 12 places may use a block of 3, 4 or 6. A line of 15 may use 3 or 5. Split the line into equal parts and see if the visible letters agree.
Step 2: write the blocks under each other
Write each block on its own row. Each column must hold the same letter. A blank takes the letter from its column.
Example: a _ c a b _ a b c _ b c has 12 places. The block has 3 letters.
| Row | Letters |
|---|---|
| 1 | a _ c |
| 2 | a b _ |
| 3 | a b c |
| 4 | _ b c |
The columns read a, b, c. The blanks are b, c, a. The answer is bca.
Step 3: try the options
Put each option into the blanks. Read the full line. The right option gives a clean repeat. First drop options whose first letter clearly fails.
Four block shapes
Fixed block. The same block repeats: abc abc abc, or pqrs pqrs. A block with a repeated letter, like baab baab, works the same way.
Growing block. Each part is longer by one letter: a, ab, abc, abcd. The line is aababcabcd. The parts have 1, 2, 3, 4 places. Or the letters repeat more: ab, aabb, aaabbb.
Mirror block. The block reads forward, then backward: pqr rqp pqr rqp. A doubled letter like rr marks the turn.
A walk that goes up and down is also a mirror. In abcdcb abcdcb the letters go up to d and come back.
Rotating block. Each block is the one before it with the first letter moved to the end: abcd, bcda, cdab, dabc. Or the last letter moves to the front: pqr, rpq, qrp.
Which block size to try
The total number of places tells you where to start.
| Total places | Try blocks of |
|---|---|
| 9 | 3 |
| 12 | 3, 4, 6 |
| 15 | 3 or 5 |
| 16 | 4 or 8 |
Example: a _ c d e a b _ d e a b c d _ has 15 places. Try blocks of 5: a _ c d e, a b _ d e, a b c d _. The block is abcde, and the blanks are b, c, e.
Blanks at the start or the end
A blank can sit in the first or last place. Do not skip it. In row form, the first blank still takes its letter from the column below or above it. The last blank takes its letter from the same column in an earlier row.
Tip: Fill the easy blanks first. Then read the line again to confirm the rest.
Checks before you mark
- Count the blanks. The answer has exactly that many letters.
- Read the whole line once. One wrong letter breaks the repeat.
- If two options fit, try another block size.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Fixed repeating block
The same short block repeats through the line. The line length is a multiple of the block size.
Count the places.
Try equal blocks and write them in rows.
Fill each blank from its column.
Read the blanks left to right.
In a fixed block every column holds one letter.
Fill the blanks: a b _ a b c _ b c a _ c
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12 places. The block abc repeats 4 times.
Row 1: a b _ so the blank is c. Row 2: a b c. Row 3: _ b c so the blank is a. Row 4: a _ c so the blank is b.
The blanks are c, a, b.
cab
Growing block
The parts get longer by one letter each time, like a, ab, abc, abcd.
Guess the parts: 1, 2, 3, 4 places.
Write the full line.
Match the blanks by place number.
The full line is known once you see the growth.
Fill the blanks: a _ b a _ c a _ c _
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10 places. Split as 1 + 2 + 3 + 4: a | ab | abc | abcd.
The full line is aababcabcd.
The blanks, in order, are a, b, b, d.
abbd
Mirror block
The block goes forward then backward, with a doubled letter at the turn.
Find the doubled letters.
Write the block forward and backward.
Fill the blanks from the repeat.
The second half of the block mirrors the first.
Fill the blanks: p _ r _ q p p q _ r _ p
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The block is pqrrqp (pqr then rqp). 12 places = 2 blocks.
Full line: pqrrqp pqrrqp.
The blanks, in order, are q, r, r, q.
qrrq
Rotating block
Each block is the last block with its first letter moved to the end.
Split the line into equal blocks.
Check how each block comes from the one before.
Write the full line.
Read the blanks.
The same letters appear in every block, in a shifted order.
Fill the blanks: a _ c b c _ _ a b
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9 places, blocks of 3: abc | bca | cab.
Full line: abcbcacab.
The blanks are place 2 (b), place 6 (a) and place 7 (c).
bac
Block with a repeated letter
The block has a doubled letter inside, like baab.
Split into equal blocks.
Write each block in a row.
Fill column by column.
Repeated letters are easy to swap. Columns keep them straight.
Fill the blanks: b a _ b _ a a b b _ a b
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12 places, blocks of 4: b a _ b | _ a a b | b _ a b.
The block is baab.
The blanks, in order, are a, b, a.
aba
Up-and-down walk
The letters climb to a peak, then come back down, like abcdcb.
Find the peak letter.
Write the block: up, then down.
Fill the blanks from the repeat.
A walk up and down is a mirror block without a doubled letter.
Fill the blanks: a b _ d c b a _ c d c _
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The block is abcdcb, 6 letters. 12 places = 2 blocks.
Full line: abcdcb abcdcb.
The blanks, in order, are c, b, b.
cbb
Shortcuts that save time
Cut the line into equal rows. Each column must hold one letter. Blanks take the letter of their column.
Fill the blanks: a _ c d a b _ d a b c _
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12 places, so try a block of 4: a _ c d, a b _ d, a b c _.
Column 1 is a, column 2 is b, column 3 is c, column 4 is d.
The blanks, from left to right, are b, c, d.
bcd
If the line has a doubled letter like rr or nn, the block probably reads forward and then backward. The block is twice the length of the first half.
Fill the blanks: m n _ m _ n n m m _ n m
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The doubled n and the doubled m suggest a mirror block: mnnm.
12 places = 3 blocks of mnnm.
The blanks, in order, are n, m and n.
nmn
Mistakes to avoid
Where most students lose marks on this subtopic.
Guessing the block size without counting the places.
Count all places first. The block size divides the total (or the parts add up to it).
Filling the blanks from right to left.
Fill from left to right. The options are written in that order.
Not reading the full line after filling.
Read the whole line once. One wrong letter breaks the repeat.
Treating a growing block as a fixed block.
If the parts get longer, split the line as 1 + 2 + 3 + 4 places.
Swapping letters in a block with a repeated letter.
Fill column by column, not from memory.
Quick revision
Read this the night before the exam.
Count total places to guess the block size: 3, 4, 5 or 6.
Write blocks under each other. Columns must match.
Four shapes: fixed, growing, mirror, rotating.
A double letter often marks a mirror turn.
Fill left to right. Read the whole line again.
Practice: 12 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 12 questions
Suggested time 9 min · wrong answers go to your mistake notebook automatically.