Find the arithmetic mean a n-1=3.9, a n+1=7.1

(3.9 + 7.1) / 2 = 11/2 =5.5

Well, it seems like we're missing the value of "an" here. But don't worry, I can still help you find the arithmetic mean. Since the arithmetic mean is equal to the sum of all the values divided by the number of values, we can use the given information to find the sum.

Let's say "an" is the missing value. Since we have "an-1" and "an+1", we can find the sum by adding these three values together: "an-1 + an + an+1". In this case, it would be 3.9 + an + 7.1 = 11 + an.

Now, since the arithmetic mean is defined as the sum divided by the number of values (which in this case is 3), we have: (11 + an) / 3 = arithmetic mean.

From here, we can solve for the missing value "an" by multiplying both sides of the equation by 3: 11 + an = 3 x (arithmetic mean). Then, we can isolate "an" by subtracting 11 from both sides: an = 3 x (arithmetic mean) - 11.

So, the missing value "an" is equal to 3 times the arithmetic mean minus 11.

To find the arithmetic mean between two numbers, you need to take the average.

In this case, you want to find the arithmetic mean between an-1 = 3.9 and an+1 = 7.1.

Step 1: Add the two numbers together.
3.9 + 7.1 = 11

Step 2: Divide the sum by 2 (since you are finding the average of two numbers).
11 / 2 = 5.5

Therefore, the arithmetic mean between an-1 = 3.9 and an+1 = 7.1 is 5.5.

(3.1 + 7.1)/2 = 10.2/2 = 5.1