Question

Precal Review

Answer 1

\[\sum_{k=1}^{5} (3k + 1)\]
\[(3 \times 1 + 1) + (3 \times 2 + 1) + (3 \times 3 + 1) + (3 \times 4 + 1) + (3 \times 5 + 1) = 50\]

Answer 2

\[\sum_{K^2 - 9}^{6} (K^2 - 9) \]
\[(3^2 - 9) + (4^2 - 9) + (5^2 - 9) + (6^2 - 9) = 50\]

Answer 3

Given a sequence 1, 8, 15

a. Write an expression for a sub n in terms of n
b. Calculate a sub 30
c. Given a sub n = 148, solve for n

Notice that the sequence is increasing by 7

7 minus what equals 1?
6

\[a _{n} = 7n - 6\]

\[a _{n} = a _{1} + (n - 1) d\]
\[a _{30} = 1 + (30 -1) 7\]
\[a _{30 } = 203\]

\[a _{n} = 148\]
\[148 = a _{1} + (n-1) d\]
\[148 = 1 + (n -1) 7\]
\[147 = (n-1) 7\]
\[21 = n-1\]
\[n = 22\]

Answer 4

Expand

\[\log _{2} (\frac{ x^3 y }{ z^2 }) = 3\log _{2}x + \log _{2}y - 2 \log _{2} z\]