# Video: Finding Five Arithmetic Means between Two Numbers

Find 5 arithmetic means between 7 and 19.

02:18

### Video Transcript

Find five arithmetic means between seven and 19.

We have two values, seven and 19. And weβve been told that there are five arithmetic means between them, which we could mark π, π, π, π, π. Our first mean is π. And we know that if π is the first mean, the distance from seven to π must be equal to the distance from π to π. And so we can say if seven plus π₯ equals π, then π plus π₯ must equal π. Moving on, π is the second mean, which means that the distance from π to π must be equal to the distance from π to π. If π plus π₯ equals π, then π plus π₯ must equal π. This must be true for all five of our arithmetic means between seven and 19. They must have a common difference. And weβre calling that common difference π₯.

If thereβs a common difference of π₯ between all five of these arithmetic means, there will also be a common difference of π₯ between the last mean π and the end of our sequence 19. We can use this information to set up an equation. We can create a relationship between seven and 19 using the common differences. To get from seven to 19, if there are five arithmetic means between them, you need to add six π₯. So weβre saying seven plus six π₯ must be equal to 19. This equation will allow us to solve for that common difference.

We subtract seven from both sides of our equation and find six π₯ equals 12, which means π₯ equals two. And if π₯ equals two, π equals nine, π equals 11, π equals 13, π equals 15, and π equals 17. And the five arithmetic means between seven and 19 are nine, 11, 13, 15, and 17.