Verbal Reasoning › Sequences
Sequences
A sequence is a row of letters or numbers that follows a hidden rule. Spot the step from one to the next and you can carry it on for ever. Everything you need is on this page.
Start here
A sequence is just a list that follows a rule. Each new item is made from the one before it by the same step every time. Once you work out the step, you can keep the list going as far as you like.
The trick is always the same: look at how you get from the first item to the second, then check that the very same change takes you from the second to the third. If it does, you have found the rule.
For letter sequences, the most useful tool is the alphabet with each letter’s position number underneath. You count along it to see how far a letter has jumped.
There are three kinds of sequence below. Each one starts with a short explanation and a worked example taken slowly, then lets you try it.
- Letter series — a row of letters that march along the alphabet by a rule.
- Number series — a row of numbers that grows or shrinks by a rule.
- Related numbers — small groups of numbers where the middle is built from the two outside ones.
1. Letter series
You are shown a row of letters and asked which letter comes next. The letters move along the alphabet by a rule. Use the alphabet strip to count each jump. Here are the patterns to watch for.
- The same jump every time. Each letter is the same number of steps along from the one before, for example 2 forward.
- A growing jump. The steps get bigger as you go: first +1, then +2, then +3, and so on.
- Going backwards. The row can move back towards A instead of forward. Forwards adds, backwards takes away.
- Letters in pairs. Sometimes the letters come in twos, and the two positions follow their own separate rules.
- Find the first jump. C to E. Count along: C, D, E. That is 2 steps forward.
- Check it stays the same. E to G is 2 forward, G to I is 2 forward. The rule is “move 2 forward” each time.
- Take one more step. I moves 2 forward to K.
A trickier kind: letters in pairs
Sometimes the letters are grouped in twos, like AZ BY CX. The secret is that the first letter of each pair follows one rule and the second letter follows another. Deal with them separately: read down the first letters, then read down the second letters.
- Read the first letters. A, B, C. Each one moves 1 forward, so the next first letter is D.
- Read the second letters. Z, Y, X. Each one moves 1 backward, so the next second letter is W.
- Put the pair together. First letter D, second letter W.
Your go: letter series
Work out the jump from the row (it might be forwards, backwards, growing, or in pairs), then choose what comes next. The alphabet strip is here to help.
2. Number series
This is the same idea with numbers. You are shown a row of numbers and asked which comes next. Look at the gap between each number and the next one. The patterns are much like the letters.
- Add the same amount. The same number is added each time, for example +5.
- Take away the same amount. The numbers get smaller by the same step, for example −4.
- A growing gap. The amount added gets bigger each time: +1, then +2, then +3.
- Doubling. Each number is the one before multiplied by 2 (or by 3).
- Two rows woven together. Every other number belongs to its own little sequence.
- Find the first gap. 4 to 7 is +3.
- Check it stays the same. 7 to 10 is +3, and 10 to 13 is +3. The rule is “add 3” each time.
- Add one more. 13 + 3 = 16.
A trickier kind: two rows woven together
If the gaps jump up and down with no steady pattern, the numbers may be two sequences taken in turns. Look at the 1st, 3rd, 5th numbers as one row, and the 2nd, 4th, 6th as another. Each row follows its own neat rule.
- Try the gaps. They jump about (+9, −7, +5…) with no steady step, so look for two woven rows.
- Read the 1st, 3rd, 5th numbers. 1, 3, 5 — this row adds 2 each time, so it carries on to 7.
- Whose turn is next? We have just had 6 (from the other row: 10, 8, 6), so the next number belongs to the 1, 3, 5 row. That is 7.
Your go: number series
Look at the gaps between the numbers, work out the rule, then choose what comes next.
3. Related numbers
Here the numbers come in small groups of three, written like (4 [12] 3). The middle number in brackets is built from the two outside numbers by a hidden rule, such as adding them or multiplying them.
You are given two complete groups so you can find the rule, then a third group with the middle number missing. Work out the rule from the first two, then use it on the last.
A little tip
Try the simple rules first, in order: do the two outside numbers add to the middle? Do they multiply to it? Does the bigger one take away the smaller? One rule must work for both of the complete groups, not just one.
(2 [6] 4) (3 [9] 6) (5 [?] 7)
- Look at the first group. 2 and 4 make 6. They could add (2 + 4 = 6), so try adding.
- Test it on the second group. 3 + 6 = 9, which is the middle number. Adding works for both, so that is the rule.
- Use it on the last group. 5 + 7 = 12.
Your go: related numbers
Work out the rule from the first two groups (it works for both), then find the missing middle number in the last group.
That is sequences
Letter series, number series and related numbers, all cracked. When you are ready, head back and pick another topic.
Back to Verbal Reasoning