Video: Finding the Next Number in a Sequence given a Two-Step Rule

The rule for the given pattern is multiply by 2, then add 7. What is the next number in 4, 15, 37, _?

02:48

Video Transcript

The rule for the given pattern is multiply by two, then add seven. What is the next number in four, 15, 37, what?

This series of numbers might not look like it, but it’s a pattern. We know this because it follows a rule. And, the rule is that we need to double it, or multiply it by two, and then add seven. This will give us our next number in the pattern before we follow the rule all over again to get the next number.

So, the pattern that we’ve been given so far starts with the number four. Four times two equals eight. And then, if we add seven to eight, we get 15. This is why the second number in our sequence is 15. To find the third number in the sequence, then, we multiply 15 by two. And, we know that 15 doubled equals 30. And then, we add seven. 30 plus seven equals 37. So, that’s why the third number in our sequence is 37.

So, to find the next number in the sequence, which is what the question asks us to do, we need to start with 37 and then follow the rule. What is 37 multiplied by two? We can partition 37 into 30 and seven. Now, we can double each part separately. 30 doubled or 30 times two equals 60. And, we know that seven doubled equals 14. Now, we just need to add the two parts together. 60 plus 14 equals 74. And so, we know that 37 multiplied by two equals 74.

Now that we know this, we just need to add seven. We know that four and six are a pair that make 10. So, 74 plus six would be 80. We don’t want to add six. We want to add one more than six, seven. So, 74 plus seven must be one more than 80. It’s 81. We found the next number in the pattern by taking the last number that we knew, which was 37, and then following the rule. First, we multiplied 37 by two. And then, we added seven. The pattern is four, 15, 37, and the next number in the pattern is 81.

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