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`