Question

1) Find
\[b(10)\] in the sequence given by
\[b(n) = -5+9(n-1)\].
\[b(10)=\]

Answer 1

To find \( b(10) \) in the given sequence defined by the formula

\[
b(n) = -5 + 9(n-1),
\]

we will substitute \( n = 10 \) into the formula.

\[
b(10) = -5 + 9(10 - 1).
\]

First, simplify the expression inside the parentheses:

\[
10 - 1 = 9.
\]

Now, substitute this value back into the equation:

\[
b(10) = -5 + 9 \times 9.
\]

Next, calculate \( 9 \times 9 \):

\[
9 \times 9 = 81.
\]

Now substitute this back into the equation:

\[
b(10) = -5 + 81.
\]

Finally, compute the sum:

\[
b(10) = 76.
\]

Thus, the value of \( b(10) \) is

\[
\boxed{76}.
\]