Question

write the next three numbers in the sequence below
-39, -31, -23, -15, -7, 1, 9, 17
what is the common difference for the sequence listed below.
common difference = 8
write the explicit formula for the sequence
t(n) = 8n - 47
what is t(77) =
when is t(n) = 825

Explanation:

Step1: Calculate t(77) via formula

Substitute \(n=77\) into \(t(n)=8n-47\):
\(t(77)=8\times77 - 47\)

Step2: Compute the value

\(8\times77=616\), so \(616-47=569\)

Step3: Solve for n when t(n)=825

Set \(8n-47=825\), rearrange:
\(8n=825+47\)

Step4: Calculate n value

\(825+47=872\), so \(n=\frac{872}{8}=109\)

Answer:

\(t(77)=569\)
\(n=109\) when \(t(n)=825\)