Sequences
Series
Sigma Notation
Series part 2
100

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

an = -9n + 7

a101 =-902

100

Find the sum:

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

3420

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

100

Find the sum:

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

165

200

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

an = 8 *(3/2)n-1

a10 = 8* (3/2)9

200

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

4 + 7 + 10 + 13 + ...

15,250

200

Write in sigma notation:

1 + 3 + 5 + ... + 199

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

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 arithmetic means:

11, _, _, _, _, 35

15.8, 20.6, 25.4, 30.2

300

Find the sum:

The positive three digit odd integers

247,500

300

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

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

300

Find the sum:

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

255 OR

-1 + 28

400

Find the geometric means:

486, _, _, _, 6

-162, 54, -18

162, 54, 18

400

Find the sum:

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

-15,146.25 OR

-384(1- (-3/2)9)


400

Write in sigma notation:

The series of positive three-digit integers divisible by 5

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

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 position of the last term:

25, 33, 41, ..., 145

145 is the 16th term.

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

500

Find the sum:

27 -18 +12 -8 + ...

81/5

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

600

Find the sum:

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

No sum

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

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