Reasoning topic
A letter series is built by a rule, like a number series, but written in letters; it is also called an alphabet series. Write each letter’s position under it, and the rule becomes arithmetic you can read.
A typical question asks for the term that fits the blank. Other questions ask for the next term, or for the one term that breaks the pattern.
Fill in the blank to complete the series: B, D, C, E, D, ?, E
F
Read the odd places and the even places apart: B, C, D, E and D, E, ?. The blank continues D, E, so it is F.
Write each letter’s position under it, from A = 1 to Z = 26. The anchors E 5, J 10, O 15, T 20 and Y 25 (EJOTY) save counting from A.
Read the positions as a number series: write the gaps, read the odd and even places apart, or look for a run you know, such as squares. A term of two or more letters runs one series in each place: read each place in the term on its own.
Past Z, start again at A: above 26, take away 26. Back past A, add 26. A letter and its opposite, such as A and Z or B and Y, add up to 27, so the opposite of a letter is 27 minus its position.
One term is missing from the series below. What is it? D, J, P, V, ?, H
Answer: B
1. One term is missing from the series below. What is it? A, A, ?, C, E, H
Write the positions. How is each one made from the two before it?
B
The positions are 1, 1, ?, 3, 5, 8. From the third term on, each is the sum of the two before it: 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8. The blank is 2, which is B.
2. Complete the series by finding the missing term: BV, CT, ?, HP, LN, QL
Each term has two letters. Read the first letters as one series and the second letters as another.
ER
First letters: B, C, ?, H, L, Q, at 2, 3, ?, 8, 12, 17. The gaps you can read are 1 (B to C), 4 (H to L) and 5 (L to Q), so the gaps run 1, 2, 3, 4, 5. The blank is 3 + 2 = 5, which is E. Check: 5 + 3 = 8, which is H.
Second letters: V, T, ?, P, N, L, at 22, 20, ?, 16, 14, 12, falling by 2. The blank is 18, which is R. The missing term is ER.
3. There is an incorrect term in the series below. Can you spot it? BAB, FEF, JIJ, MMN, RQR
Read each term in three places: the first letters, the middle letters and the last letters.
MMN
Middle letters: A, E, I, M, Q, at 1, 5, 9, 13, 17, rising by 4. First letters: B, F, J, M, R, at 2, 6, 10, 13, 18. Leave out M and 2, 6, 10, _, 18 rise by 4, so the fourth term’s first letter should be 14, which is N.
In every other term the last letter repeats the first, so the fourth term should be NMN. MMN is the incorrect one.
Practise Letter Series in the app. The questions follow your level, and what you practise comes back just before you'd forget it.
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