Question 3 of 13 Which represents the explicit formula for the arithmetic sequence a n = 15 + 5 ( n − 1 ) a n = 15 + 5 n - 1 in

Question

Tamiku [17]

3 years ago

10

Question 3 of 13 Which represents the explicit formula for the arithmetic sequence a n = 15 + 5 ( n − 1 ) a n = 15 + 5 n - 1 in

function form?

Mathematics

1 answer:

tatyana61 [14] · Answer 1 · 2022-05-18T07:20:23+03:00

tatyana61 [14]3 years ago

3 0

Answer:

$\textbf{Option C: \mathmode{\mathit{f(n) = 5n + 10}}}\\$

Step-by-step explanation:

$\textrm{There are two simple ways to solve the equation:}\\{\underline{\textbf{Method I:}}\hspace{3mm} \textup{\textrm{ Substitute \mathmode{n = 1} in the equation{\mathit{a} = 15 + 5(n - 1)}}}}\\\textup{\textrm{i.e., \mathrm{a = 15 + 5(0) = 15}}}\\\\$

$\textup{\textrm{In the options, again substitute \mathbf{n = 1}.}}\\\textup{\textrm{We can easily see that only Option \mathbf{C} satisfies the equation and renders 15. }}\\\textup{\textrm{Now for \textbf{\underline{Method II:}}\textup{\textrm{Simplify the given equation into \mathit{a = 15 + 5n - 5}}}}}\\\implies \textup{\textrm{a = 5n + 10}}\\$