Answer:
Option D: - 6; [tex]$ \textbf{-5}\frac{\textbf{5}}{\textbf{2}} $[/tex]; [tex]$ \textbf{-4}\frac{\textbf{1}}{\textbf{5}} $[/tex].
Step-by-step explanation:
The sequence is defined by:
[tex]$ A(n) = -6 + (n - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]
To find the first term of the sequence simply substitute n = 1.
First term of the sequence:
[tex]$ A(1) = -6 + (1 - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]
[tex]$ = - 6 $[/tex]
Fourth term of the sequence:
[tex]$ A(2) = -6 + (4 - 1) \bigg ( \frac{1}{5} \bigg) $[/tex]
[tex]$ = - 6 + 3\bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = \frac{- 30 + 3}{5} $[/tex]
[tex]$ = \frac{-27}{5} $[/tex]
[tex]$ = \frac{-25 - 2}{5} $[/tex]
[tex]$ = - 5 - \frac{2}{5} $[/tex]
[tex]$ = -5\frac{2}{5} $[/tex] is the required answer.
Tenth term of the sequence:
[tex]$ A(10) = - 6 + (10 - 1) \bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = - 6 + 9\bigg( \frac{1}{5} \bigg) $[/tex]
[tex]$ = \frac{-30 + 9}{5} $[/tex]
[tex]$ = \frac{-21}{5} $[/tex]
[tex]$ = \frac{-20 - 1}{5} $[/tex]
[tex]$ = - 4 - \frac{1}{5} $[/tex]
[tex]$ = -4\frac{1}{5} $[/tex] is the required answer.
