Easy. "Consecutive" means "in an unbroken sequence". So consecutive numbers means numbers that are right next to each other, for instance 34, 35, 36, 37 and 38 are five consecutive whole numbers; 2, 4, 6, 8, 10 are five consecutive even numbers; and 13, 15, 17, 19 are four consecutive odd numbers.
So consecutive numbers form a sequence, which has a quick way to add up. You have learned how to solve problems like this:
2 + 3 + 4 + 5 + 6 + 7 + 8 = (2+8) + (3+7) + (4+6) + 5 = 10+10+10+10+5 = 45
The trick is to find pairs of 10 such as 2+8 or 3+7. In general, if you are adding or subtracting a sequence of numbers, regrouping can reduce your work. How would you regroup the following expressions to make calculation easier?
32+34+36+38+40+42
128+138+148+158+168
84+81+78+75+72
100-1-9-2-8-3-7-4-6-5-5-6-4-7-3-8-2-9-1
1000-81-19-82-18-83-17-84-16-85-15-86-14-87-13-88-12-89-11
12+13+14+15+......+28+29+30+31 (adding all consecutive numbers between 12 and 31)
Three consecutive odd numbers add to 45, what are the three numbers?
Four consecutive even numbers add to 52, what are these numbers?
Eve won an award so she plans to eat cookies every day in October. She will eat 2 cookies on Oct 1, and each day, she will eat 2 more cookies than the previous day. How many cookies will she eat on Oct 31? How many cookies her mom will have to buy for her in October?
In a baseball stadium, there are 100 seats in the row 1, 120 seats in row 2, 140 seats in row 3..., each row will have 20 more seats than the previous row. There are a total of 10 rows in the stadium, how many people can watch a baseball game together?
Now, what if the sequences grow longer? Look at these two problems. You can easily regroup the first expression as 1 + (3 - 2) + (5 - 4) + (7 - 6) ... + (2019 -2018), but how many pairs are here?(Hint: there are 2019 numbers from 1 to 2019. Since even and odd numbers alternate, there should be the same amount of even and odd numbers except for the very last.)
This one is similar:
