Answer:
[tex]a =7.51+ 0.35(n - 1)[/tex]
Step-by-step explanation:
The arithmetic sequence has the form:
[tex]a =a_1 + d(n - 1)[/tex]
When a=10.31, n=9, we substitute to get:
[tex]a_1 + 8d = 10.31....eqn1[/tex]
Similarly, when n=13 and a=11.71, we get:
[tex]a_1 + 12d= 11.71....eqn2[/tex]
Subtract equation 1 from equation 2 to get:
[tex]4d = 1.4[/tex]
This implies that
[tex]d = 0.35[/tex]
Substitute into the second equation to get:
[tex]a_1 +12(0.35) = 11.71[/tex]
Solve to get
[tex]a_1 = 7.51[/tex]
Hence the explicit formula is:
[tex]a =7.51+ 0.35(n - 1)[/tex]
