Sequences & Series Review

1

100

What is the formula for an Arithmetic Sequence?

a_n = a₁ + (n - 1)d

200

Write an explicit formula for the following sequence:
-24, -20, -16, ...

T_n=4n-28

300

How many terms are in the following sequence? 1,3,5,7...43

22 terms

400

Nolan is eating a pack of skittles. This pack has 2 green, 3 red, 6 purple, 3 yellow, and 1 orange skittle. However, Nolan does not like purple skittles. Find P(not purple).

9/15 = 3/5

2

100

What is the forumla for an Arithmetic Series

S_n=(n/2)(a₁+a_n

200

Find the sum of the following sequence: 1,2,3,4,5,6....111,112,113,114

6555

300

Find S₉₈ for the following series:
0.2, 0.4, 0.6, ...

970.2

400

Write the equation and find the sum of this series
8.9,17.8,26.7,35.6,44.5 ... 1619.8

a_n=8.9n
S_n=(182/2)(8.9+1619.8)

3

100

Ike has 12 shirts. He has 5 blue shirts, 2 green shirts, 4 white shirts, and 1 red shirt. Find P(blue shirt).

5/12

200

Write a recursive formula for the following sequence: 8, -4, 2, -1, ...

T1=8 Tn=(-1/2)*Tn-1

300

What is the 17th term of the following sequence? 65, 45.5, 31.85, 22.295, ...

0.22

400

What is the equation to find the 89^th term of this sequence?

3, 15, 75, 375

3*5^89-1

4

200

Find the sum of the following sequence: 3, 12, 48, ... , 196608

262,143

400

Holden is playing with a deck of cards. What is the probability of Holden drawing a Queen out of the deck?

4/52

Binomial Theorem

100

Expand (x+y)⁶

x⁶+6 x⁵ y+15 x⁴ y²+20 x³ y³+15 x² y⁴+6 x y⁵+y⁶

200

Find the 3rd term of (x+3y)⁹

324x⁷y²

300

(2x+1)⁵

32n⁵ + 80n⁴ + 80n³ + 40n² + 10n + 1

400

(y³ − 4x)³

y^{9 − 12y63x2 − 64x3}