Respuesta :
Answer:
Option A is correct.
[tex]a_n = \frac{5}{2}n - \frac{11}{2}[/tex]
[tex]a_{17}=37[/tex]
Step-by-step explanation:
An arithmetic sequence is a sequence of number that the common difference between between the consecutive term is constant.
Explicit formula for arithmetic sequence is given by;
[tex]a_n = a_1 + (n-1)d[/tex]
where
n is the number of terms.
[tex]a_1[/tex] is the first term
d is the common difference.
Given the sequence : [tex]a_n = \{-3, -\frac{1}{2}, 2, \frac{9}{2} , 7, ....\}[/tex]
This is an arithmetic sequence with common difference: d = [tex]\frac{5}{2}[/tex]
Here, [tex]a_1 = -3[/tex]
Since;
[tex]-\frac{1}{2} - (-3) = -\frac{1}{2}+3 = \frac{5}{2}[/tex]
[tex]2- (-\frac{1}{2}) = 2+\frac{1}{2} = \frac{5}{2}[/tex] and so on...
Then;
[tex]a_n = a_1+(n-1)\frac{5}{2}[/tex]
or
[tex]a_n = -3+\frac{5}{2}n -\frac{5}{2}[/tex]
Simplify:
[tex]a_n = \frac{5}{2}n - \frac{11}{2}[/tex] .....[1]
To find [tex]a_{17}[/tex];
put n =17 in [1] we get;
[tex]a_{17} = \frac{5}{2}(17) - \frac{11}{2} = \frac{85}{2} - \frac{11}{2} = \frac{85-11}{2}=\frac{74}{2} = 37[/tex]
Therefore, the explicit formula for the given sequence is, [tex]a_n = \frac{5}{2}n - \frac{11}{2}[/tex] and value of [tex]a_{17} = 37[/tex];
