Observe the sequence: \[
1,\ 11,\ 21,\ 1211,\ 111221,\ 312211,\ 13112221
\] What is the next term?
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The "look and say" sequence
It has the appeal of patterns that seem almost visible and yet slip away for a moment longer. There is no hidden algebra here: just learn to look at the row with the correct rhythm.
Hints
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- It is not added or multiplied: each term is obtained by reading the previous one.
- The reading is done by groups of consecutive equal figures.
Solution
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Answer: the next term is 1113213211. The rule is to describe the previous term by counting groups of consecutive equal digits.
For example, 13112221 is read as:
- a 1 ->
11 - a 3 ->
13 - two 1 ->
21 - three 2 ->
32 - a 1 ->
11Concatenating:11 13 21 32 11=> 1113213211. This sequence is known as look-and-say (or Morris sequence).
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