Answer:
The 28th term is [tex]\boxed{63.8}.[/tex]
Step-by-step explanation:
Let [tex]a_n[/tex] denote the [tex]n[/tex]th term of the sequence.
We can start by noticing that:
[tex]a_2 - a_1 = a_3 - a_2 = a_4 - a_3 = 2.6 = r,[/tex]
which means that this sequence is actually an arithmetic progression. We know that the [tex]n[/tex]th term of these sequences is always:
[tex]a_n = a_1 + r(n-1).[/tex]
This sequence in particular is given by:
[tex]a_n = -6.4 + 2.6 (n-1).[/tex]
To find the 28th term, we simply set [tex]n=28[/tex]:
[tex]a_{28} = -6.4 + 2.6 (28-1) = -6.4 + 2.6 \times 27 = -6.4 + 70.2 = 63.8.[/tex]
So we finally get:
[tex]\boxed{a_{28} = 63.8}.[/tex]
