Answer
* To find the two arithmetic means, let's solve for the common difference first. To solve the common difference, we need to use the formula d=an-ak/n-k.
- [tex]d = \frac{a_{n} - a_{k} }{n - k} [/tex]
- [tex]d = \frac{a_{4} - a_{1} }{4 - 1} [/tex]
- [tex]d = \frac{1 - ( - 5)}{3} [/tex]
- [tex]d = \frac{6}{3} [/tex]
- [tex]d = 2[/tex]
The commen difference is 2.
* Now let's find the two arithmetic means.
- [tex]a_{2} = a_{1} + d = - 5 + 2 = - 3[/tex]
- [tex]a_{3} = a_{2} + d = - 3 + 2 = - 1[/tex]
~ The two arithmetic means between -5 and 1 are -3 and -1.
