Sequences and Series Review

Arithmetic

100

The common difference of this arithmetic series: 12+24+36+48+60....

What is 12?   

200

The explicit formula for an arithmetic sequence

What is 

a_n=a_1+d(n-1)?

300

Write the first five terms of the sequence. 

a_1=-25; a_k=a_(k-1)-7

a_1=-25, a_2=-32, a_3=-39, a_4=-46, a_5=-53

400

The term number of

-57

in the sequence 6,-1,-8,-15-....-57.

What is the 10th term?  

500

Find the 8th partial sum of the following arithmetic sequence. A1=5 A5=17 (Calc)

Sn= 124

Geometric

100

The common ratio of

10,2,2/5,2/25,...

What is 

1/5?

200

The common ratio if the first term is 4 and the third term is 36.

What is 3?

300

The explicit formula for the sequence where

a_1=12

and

a_2=30

What is 

a_n=12(5/2)^(n-1)?

400

The 10th term of the geometric sequence where

a_1=1

and

a_4=8

What is 512?

500

The explicit form of the sequence where the 6th term is 

9/4

and the 11th term is 

8/27

What is 

a_n=2187/128?

Sigma Notation

100

The number of terms in the series 

sum_(k=1)^16 (3k+1)

What is 16?

200

sum_(i=1)^5 (3k+1)

What is 50?

300

The sigma notation representation of the following series:

5+5/6+5/36+5/216+5/296

What is 

sum_(n=1)^5 5(1/6)^(n-1)?

400

sum_(j=1)^oo 9(1/3)^(j-1)

What is 

500

sum_(n=2)^8 6(3)^(n-1)

What is 19,674?

Factorial

100

5!

What is 120?

200

(9!)/(4!)

What is 15,120?

300

(10!)/(7!6!)

What is 1?

400

The first three terms of 

(n+1)!

What are 

n+1,n, and n-1?

500

((2z-2)!)/(2z!)

What is 

1/((2z-1)(2z))?

Recursive

100

The recursive formula for 1, 8, 15, 22, ...

What is 

a_1=1; a_k=a_(k-1)+7?

200

The 6th term of the sequence 

Sn= 192

300

A skydiver with no air resistance jumps from an airplane. During the first second of fall, he falls 5.3 meters, during the second second, he falls 14 meters, during the third second, he falls 22.7 meters, and during the fourth second, he falls 31.4 meters. If this continues, how many meters would he have fallen total in 12 seconds.

Sn=678.6 meters

400

You go to work for the Cleveland Cavaliers, they pay you $.01 the first day, $.04 the second day, $.16 the third day and so on. If the daily wage keeps quadrupling, what will your total income be after 17 days?

Sn= $57,266,230.61

500

A deposit of $30 is made at the beginning of each month in account the pays 6% interest compounded monthly. The balance A in the account at the end of 10 years is given by A=30(1+.06/12)+.....+....+30(1+.06/12)^120 Find A.

Sn=$4940.96