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Detective Math is on a new case! She needs to crack some number sequence codes to solve the mystery.
Can you help her with the following clues?
a) Find three consecutive even numbers that have a sum of 222.
b) Discover four consecutive odd numbers that add up to 112.
c) Uncover five consecutive whole numbers with a sum of 1010.
d) If the sum of six consecutive numbers is 111, what is the smallest number in the sequence?
Remember, Detective Math always shows her work to prove she’s solved the case correctly!
Here’s how Detective Math cracked the codes:
a) Three consecutive even numbers with a sum of 222:
– Divide 222 by 3 to find the middle number: 222 ÷ 3 = 74
– The three numbers are 72, 74, and 76
– Proof: 72 + 74 + 76 = 222
b) Four consecutive odd numbers that add up to 112:
– Divide 112 by 4 to find the average: 112 ÷ 4 = 28
– The middle two numbers are 27 and 29
– The four numbers are 25, 27, 29, and 31
– Proof: 25 + 27 + 29 + 31 = 112
c) Five consecutive whole numbers with a sum of 1010:
– Divide 1010 by 5 to find the middle number: 1010 ÷ 5 = 202
– The five numbers are 200, 201, 202, 203, and 204
– Proof: 200 + 201 + 202 + 203 + 204 = 1010
d) Six consecutive numbers with a sum of 111:
– Let x be the smallest number in the sequence
– The sum can be written as: x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 111
– Simplify: 6x + 15 = 111
– Solve for x: 6x = 96, so x = 16
– The sequence is 16, 17, 18, 19, 20, 21
– Proof: 16 + 17 + 18 + 19 + 20 + 21 = 111
Case closed! Detective Math has successfully solved all the number sequence mysteries!
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