Question

Find the number of A.Ms. between 5 and 83. If the ratio between the first A.M. and the last A.M. is 1:7.​

Answer 1

This sounds like an old school type of question. You are asking to create an arithmetic sequence with first term 5 and last term 83 without knowing either d or n.

So, a = 5 and a + (n − 1)d = 83. The first mean is 5 + d and the last mean is 83- d and 83 - d we insist that 5+d = 7 . Thus, 83d 35 + 7d and d = 6. From that, 5 + 6(n − 1) = 83 and n = 14. However, that includes Both the first and last terms. So there are 12 means inserted.