## How to Solve Consecutive Number Problems Part 2

In the previous post, we have discussed the basics of consecutive number problems. We have learned that in word problems in Algebra, consecutive numbers usually mean numbers increasing  by 1. Consecutive even numbers and consecutive odd numbers increase by 2. So, consecutive numbers whose smallest is x are x, x + 1 and x + 2 and so on, while consecutive odd/even numbers whose smallest number is y are y, y + 2, y + 4 and so on.

In this post, we begin with the third example in the series since we already had 2 examples in the previous post.

Example 3

The sum of four consecutive numbers is 70. What are the numbers?

Solution

Let

$x$ = first number

$x + 1$ = second number

$x + 2$ = third number

$x + 3$ = fourth number

Since we are talking about the sum of the four numbers, we add them. That is,

sum of four numbers = 70

$x + (x + 1) + (x + 2) + (x + 3) = 70$

Simplifying, we have

$4x + 6 = 70$

$4x = 70 - 6$

$4x = 64$

$4x/4 =64/4$

$x = 16$.

So, the smallest number is 16. Therefore, the four consecutive numbers are 16, 17, 18, and 19.

Check: $16 + 17 + 18 + 19 = 70$

Example 4

The sum of 3 consecutive odd numbers is equal to 51. What are the numbers?

Solution

As we have discussed above, odd numbers increase by 2 each time (like 5, 7, 9, 11), so we let

$x$ = first number

$x + 2$ = second number

$x + 4$ = third number

Now, we add the numbers and equate to 51.

$x + (x + 2) + (x + 4) = 51$

$3x + 6 = 51$

$3x = 51 - 6$

$3x = 45$

$3x/3 = 45/3$

$x = 15$

So the smallest odd number is 15. Therefore, the three consecutive odd numbers are 15, 17, and 19.

Check: $15 + 17 + 19 = 51$

You can also view the video tutorial of the discussion above in this video. The language is in Taglish.

In the next post, we will be discussing more problems about consecutive numbers.

## How to Solve Consecutive Number Problems Part 1

This is the first of the Solving Consecutive Number Series, a series of post discussing word problems about consecutive numbers.

Consecutive numbers are numbers that follow each other in order. In number problems in Algebra, consecutive numbers usually have difference 1 or 2. Below are the types of consecutive numbers,

consecutive numbers – 5, 6, 7, 8, …

consecutive even numbers – 16, 18, 20, 22…

consecutive odd numbers – 3, 5, 7, 8, …

The symbol … means that the list may be continued.

Notice that consecutive numbers always increase by 1 in each term. If we make 5 as point of reference, then, we can write the numbers above as

5, 5 + 1, 5 + 2, 5 + 3.

That means that if our first number is x, then the list above can be written as

x, (x + 1), (x + 2), (x + 3)