While exploring a winding valley, Emek and Luna found a row of ranger signal posts that marked the safe hiking route. Some of the numbers on the posts had faded, leaving gaps in the sequence: 45, 60, 75, __, 105. They studied the changes between the numbers and discovered that each post increased by 15. Emek and Luna used this rule to replace the missing sign and checked the rest of the route. With the correct numbers restored, future hikers could follow the valley path without getting lost.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Find how much each number increases from one post to the next.
The ranger signal posts show the pattern 45, 60, 75, __, 105. What number is missing?
859095100Correct! The pattern increases by 15, so 75 + 15 = 90.
Check the difference between neighboring numbers. The same amount is added each time.
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Hint
Continue adding 15 until you reach the sixth number in the sequence.
The first signal post shows 45. If the pattern continues by adding 15 for each new post, what number will be on the sixth signal post?
Correct! The sequence is 45, 60, 75, 90, 105, 120.
Count the posts carefully and add 15 each time.
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Hint
Look for the rule that connects every pair of numbers in the sequence.
A hiker says the missing signal post should be 95 because the numbers are getting larger. Why is this not correct?
Because the pattern should decrease by 15 insteadBecause all numbers in the pattern must be evenBecause the increase between posts must stay the sameBecause the first number should be changedCorrect! A pattern follows a consistent rule, and this one increases by 15 each time.
The important part of a number pattern is keeping the same rule throughout.
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