Number and Letter Series
Spot arithmetic, geometric, and alternating patterns in number and letter series.
What you'll learn
- Identify whether a number series has a constant difference (arithmetic) or a constant ratio (geometric)
- Continue a letter series by converting letters to alphabet positions and back
- Recognize an alternating series made of two interleaved patterns
Explanation
A series is a sequence of items that follow a rule. Placement tests use series questions to check whether you can find that rule from a handful of examples and apply it one step further.
Arithmetic series have a constant difference between consecutive terms. In 3, 7, 11, 15, ?, each term is 4 more than the last, so the next term is 15 + 4 = 19. Geometric series have a constant ratio instead: in 2, 6, 18, 54, ?, each term is 3 times the last, so the next term is 54 * 3 = 162.
Letter series work the same way once you convert letters to numbers. Map A=1, B=2, ..., Z=26. The series B, D, F, H, ? becomes positions 2, 4, 6, 8, an arithmetic series with a constant difference of 2, so the next position is 10, which is J.
Not every series is that simple. Some are alternating series built from two separate patterns interleaved together. In 1, 3, 8, 10, 15, ?, look at every other term: the odd positions (1, 8, 15) increase by 7 each time is wrong at a glance -- instead notice the actual step pattern alternates +2, +5, +2, +5, ...: 1 +2= 3, 3 +5= 8, 8 +2= 10, 10 +5= 15, so the next step is +2, giving 17.
The reliable method is always the same three steps: compute the difference (or ratio) between each consecutive pair, check whether that difference is constant, and if it isn't, check whether it alternates between two constant values before assuming the series is random. Never commit to a rule from just two terms -- always verify it against a third.
Example
Finding the next term in a constant-difference series.
function nextInArithmeticSeries(series) {
const step = series[1] - series[0];
return series[series.length - 1] + step;
}
// nextInArithmeticSeries([3, 7, 11, 15]) -> 19Guided exercise
Guided exercise
Write isArithmeticSeries(series) that returns true if every consecutive pair of terms in the array has the same difference (length is always >= 2), and false otherwise.
Checks: Detects a genuine arithmetic series · Rejects a geometric series · plus 1 hidden check
Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.
Stuck? Get a hint.
Independent exercise
Independent exercise
Write nextLetterInSeries(letters) where letters is an array of uppercase single-character strings whose alphabet positions (A=1 ... Z=26) form an arithmetic series. Return the next letter as a single uppercase character. Assume the result never exceeds 'Z'.
Checks: Continues a 4-letter series with step 2 · Continues a 3-letter series with step 2 · plus 1 hidden check
Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.
Stuck? Get a hint.
Common mistakes
- Assuming a series is arithmetic after checking only the first two terms, without verifying a third.
- Off-by-one errors when converting letters to positions -- remember A is position 1, not 0.
- Missing that a series alternates between two interleaved patterns instead of following one constant rule.
Knowledge check
Takeaway
Every series question comes down to finding the rule between consecutive terms and verifying it against at least three terms before trusting it.
Summary
Number series are arithmetic (constant difference), geometric (constant ratio), or alternating (two interleaved patterns). Letter series follow the same logic once converted to alphabet positions.
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