Number and letter series for SSC GD

A series is a list of numbers or letters that follows one rule. You find the rule from the terms you can see, then use it to get the next term. The good news for SSC GD is that the rules are simple. You will rarely need anything beyond adding, multiplying, squares and cubes.

What costs marks is not difficulty but guessing. Candidates spot a rule that fits the first two gaps, write the answer, and never check the rest. This guide gives you a fixed order of checks so you stop guessing.

The checking order

Work down this list. One of these fits almost every SSC GD series.

1. Constant difference. Subtract each term from the next. Are the gaps the same?
2. Constant ratio. Divide each term by the one before. Is it always × 2, × 3 or ÷ 2?
3. Differences that grow. Are the gaps 1, 2, 3, 4 or 2, 4, 6, 8 or 3, 5, 7, 9?
4. Squares and cubes. Are the terms n², n³, or one more or one less than them?
5. Mixed operation. Is it × 2 + 1, or × 2, × 3, × 4?
6. Two series mixed. Do the odd places and the even places follow separate rules?

Eight common patterns

Notice that some series fit two descriptions. 2, 5, 10, 17, 26 is "square plus one" and also "gaps of 3, 5, 7, 9". Both give 37, so there is no conflict. If two rules ever give different answers, check which one fits every term and which one appears in the options.

Letter series

Turn letters into numbers first. A = 1, B = 2 … Z = 26. The EJOTY trick gets you there fast: E = 5, J = 10, O = 15, T = 20, Y = 25. Every other letter is one or two steps from one of these.

If a count goes past Z, go round again: Z + 1 = A, so 27 = A, 28 = B. If it goes below A, A − 1 = Z.

Solved examples

Example 1 (growing differences). 4, 7, 12, 19, 28, ?

1. Gaps: 3, 5, 7, 9. These are odd numbers going up by 2.
2. The next gap is 11.
3. 28 + 11 = 39.
4. Check: the terms are also n² + 3 (1 + 3, 4 + 3, 9 + 3 …), and 6² + 3 = 39. Both views agree.

Example 2 (changing multiplier). 3, 6, 18, 72, ?

1. 3 × 2 = 6. 6 × 3 = 18. 18 × 4 = 72.
2. The multiplier goes up by 1 each time, so the next is × 5.
3. 72 × 5 = 360.

Example 3 (subtracting squares). 100, 96, 87, 71, ?

1. Gaps: −4, −9, −16. These are 2², 3², 4².
2. The next gap is −5², which is −25.
3. 71 − 25 = 46.

Example 4 (two series mixed). 5, 20, 7, 18, 9, 16, ?

1. Odd places (1st, 3rd, 5th): 5, 7, 9. They go up by 2.
2. Even places (2nd, 4th, 6th): 20, 18, 16. They go down by 2.
3. The missing term is the 7th, an odd place. After 9 comes 11.

Example 5 (letters). B, D, G, K, ?

1. Positions: 2, 4, 7, 11.
2. Gaps: 2, 3, 4. The next gap is 5.
3. 11 + 5 = 16, which is P.

Example 6 (wrong number). Find the wrong number: 2, 5, 10, 17, 26, 38, 50

1. Test square plus one: 1² + 1 = 2, 2² + 1 = 5, 3² + 1 = 10, 4² + 1 = 17, 5² + 1 = 26.
2. The next should be 6² + 1 = 37, then 7² + 1 = 50.
3. 50 fits, so the rule holds. The wrong number is 38.

Common mistakes

Practice set

1. 6, 12, 18, 24, ?
2. 3, 9, 27, 81, ?
3. 1, 2, 4, 7, 11, ?
4. 0, 3, 8, 15, 24, ?
5. 4, 9, 19, 39, ?
6. B, E, H, K, ?
7. Z, X, U, Q, ?
8. Find the wrong number: 3, 6, 12, 24, 46, 96

Answers:

1. 30. Add 6 each time.
2. 243. Multiply by 3: 81 × 3 = 243.
3. 16. Gaps 1, 2, 3, 4, so the next gap is 5.
4. 35. Square minus one: 6² − 1 = 35. The gaps 3, 5, 7, 9, 11 agree.
5. 79. Double and add one: 39 × 2 + 1 = 79. The gaps 5, 10, 20, 40 agree.
6. N. Positions 2, 5, 8, 11, so the next is 14.
7. L. Positions 26, 24, 21, 17; gaps −2, −3, −4, so the next gap is −5 and 17 − 5 = 12.
8. 46. Each term doubles: 24 × 2 = 48, and 48 × 2 = 96.

What to do next

• Learn squares to 30 and cubes to 15 (see squares and square roots).
• Write the alphabet with positions from memory until it takes under a minute.
• Solve 25 series questions a day for a week, writing the gap row every time.
• Try missing numbers next, which uses the same rules inside tables and figures.