Algebra 2 Unit 10 Review

Sequences

100

Find the formula for the nth term and then find the 101st term:-2, -11, -20, ...

a_n = -9n + 7

a₁₀₁ =-902

200

Find the formula for the nth term and then find the 10th term: 8, 12, 18, 27, ...

a_n = 8 *(3/2)^n-1

a₁₀ = 8* (3/2)⁹

300

Find the arithmetic means:

11, _, _, _, _, 35

15.8, 20.6, 25.4, 30.2

400

Find the geometric means:

486, _, _, _, 6

-162, 54, -18

162, 54, 18

500

Find the position of the last term:

25, 33, 41, ..., 145

145 is the 16th term.

600

A pile of bricks has 85 bricks in the bottom row, 79 bricks in the second row, 73 bricks in the third row, and so on until there is only 1 brick in the top row. 

a. How many bricks are in the 12th row?

b. How many rows are there in all?

a. 19 bricks

b. 15 rows

700

A new pair of running shoes costs $70 now. Assuming an annual 8% price increase, find the price 15 years from now. 

70*1.08¹⁵

Series

100

Find the sum:

-12 + -7 + -2 + ... + 183

3420

200

Find the sum of the first 100 terms of the series:

4 + 7 + 10 + 13 + ...

15,250

300

Find the sum:

The positive three digit odd integers

247,500

400

Find the sum:

sum_{n=1}^9 (640 (-3/2)^{n})

-15,146.25 OR

-384(1- (-3/2)⁹)

500

Jill pays $1500 for rent each month. Every year, the rent increases by $50. How much has she paid for rent over 20 years?

$474,000

600

Find the sum:

3 + 4 + 5 1/3 + 7 1/9 + ...

No sum

Sigma Notation

100

Write the series in expanded form. Don't calculate the sum.

\sum_{n=5}^10 (\frac{3n}{n+1})

5/2 +18/7 + 21/8 +8/3 +27/10 + 30/11

200

Write in sigma notation:

1 + 3 + 5 + ... + 199

\sum_{n=1}^100 (2n-1)

300

Write in sigma notation: 6 -12 + 24 - ... -192

sum_{n=1}^6 6(-2)^{n-1}

400

Write in sigma notation:

The series of positive three-digit integers divisible by 5

sum_{n=1}^180 (5n+95)

Series part 2

100

Find the sum:

sum_{m=10}^20 (30-m)

165

200

Find the sum:

2 -6 + 18 - 54 + 162 -486 + 1458 - 4374 + 13122 - 39366

-29,524 OR

1/2(1-(-3)¹⁰)

300

Find the sum:

1 + 2 + 4 + 8 + ... 128

255 OR

-1 + 2⁸

400

Peter works for a house building company for 4 months per year. He starts out making $3,000 per month. At the end of each month, his salary increases by 5%. How much money will he make in those 4 months?

$12,930.38 OR

-60000( 1-1.05⁴)

500

Find the sum:

27 -18 +12 -8 + ...

81/5

600

A bouncy ball decreases in height by 5% on each bounce. On the first bounce, the ball goes up and down 12 m (so 24 m in total). How far does the ball travel before it stops bouncing?

480 m