Question

I need help with this question. I need to find the common difference, the term named in the problem, and the explicit formula. Thank you

Answer 1

From the question,

We are given the sequence

$-33,-28,-23,-18,\ldots$

From the sequence, the common difference, d is

$d=-28-(-33)=-23-(-28)=-18-(-23)=5$

Therefore,

Common difference = 5

The explicit formula of an arithmetic sequence is given as

$a_n=a_1+d(n-1)$

Where,

a(1) = first term

a(n) = nth term

d = common difference

From the sequence

$a_1=-33,d=5$

Therefore, the explicit formula is

$\begin{gathered} a_n=-33+5(n-1) \\ a_n=-33+5n-5 \\ a_n=-38+5n \end{gathered}$

Therefore, the explicit formula is

$a_n=-38+5n$

Finally, we are to find a(27)

This will be done by using the explicit formula

Hence

$\begin{gathered} a_{27}=-38+5n \\ n=27 \\ a_{27}=-38+5(27) \\ a_{27}=-38+135 \\ a_{27}=97 \end{gathered}$

Therefore,

$a_{27}=97$