Question

find the arithmetic means of the sequence 23, , , , 67

Answer 1

Subtract the first term from the last and divide by the number of spaces the last term is from the first term

Answer 2

Try counting up numbers until you get the right answer in the right amount of spaces.

Answer 3

I believe the answer is 11.

Answer 4

How do you even get 11?

Answer 5

THe mean MUST be between the lowest and highest number - it cannot be 11

Answer 6

The idea is to write the sequence first, since it is an arithmetic sequence, we can use the formula \[a_n = a_1+d(n-1)\] so here \[a_1 = 23, a_n=67, \text{and the value of n is given by the number of spaces, so we have n = 5}\] We can then plug all those values and solve for d. \[67 = 23+d(4)\] if we solve that we get d = 11, that means the difference between each term of the sequence is 11, so for example if the first term of the sequence is 23, the second one will be 23+11 so 34, that means the sequence will be \[23,34,45,56,67\]. Now that we have the full sequence we can proceed obtaining the arithmetic mean, that would be the sum of all terms of that sequence divided by the number of terms, so we have: \[Mean = \cfrac{23+34+45+56+67}{5}\\ Mean = 45\]