Question

Find an equation for the nth term of the arithmetic sequence.

-17, -12, -7, -2, ...

a. an = -17 + 5(n + 2)

b. an = -17 + 5(n + 1)

c. an = -17 + 5(n - 1)

d. an = -17 x 5(n - 1)

Answer 1

what do you think is the common ratio?

Answer 2

common difference, I hope you mean :-)'

Answer 3

i dont know how to do the problem pretty much at all is there a formula??

Answer 4

is the answer d?

Answer 5

common ratio/difference :)
meaning

is the 2nd term bigger or smaller than the 1st one? by how much?

what about the 3rd term and 2nd, is it bigger or smaller? by how much?

Answer 6

bigger by 5

Answer 7

so 5 is our common ratio or difference

so you get the next term, by simply ADDING +5 to the current terms
thus the "common difference"

anyhow, we know the 1st term value is -17

thus \(\Large \bf a_{\color{red}{ n}}=a_1+({\color{red}{ n}}-1){\color{blue}{ d}}
\\ \quad \\

{\color{blue}{ d}}=\textit{common difference}\qquad \qquad a_1=\textit{first term}
\\ \quad \\
\Large a_{\color{red}{ n}}=-17+({\color{red}{ n}}-1)({\color{blue}{ 5}})\)

Answer 8

okay, i see. how do you know the part in the parenthesis is n-1

Answer 9

well, you're not asked for find an \(\bf n^{th}\) term, just to provide the arithmetic sequence equation with that common difference and 1st term

Answer 10

say for example if you wanted to find the 27th term and say the 35th term or 11th term
then you'd just use \(\bf a_{\color{red}{ 27}}=-17+({\color{red}{ 27}}-1)({\color{blue}{ 5}})
\\ \quad \\
a_{\color{red}{ 35}}=-17+({\color{red}{ 35}}-1)({\color{blue}{ 5}})
\\ \quad \\
a_{\color{red}{ 11}}=-17+({\color{red}{ 11}}-1)({\color{blue}{ 5}})\)

Answer 11

okay, so the answer would be c?

Answer 12

okay, so the answer would be c? \(\checkmark\)

Answer 13

thank you so much i understand now:)

Answer 14

yw