1.

 Quantity A Quantity B The sum of the odd integers from 1 to 199 The sum of the even integers from 2 to 198

2. The sequence of numbers { a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 }… { a }_{ n }.. is deﬁned by { a }_{ n }=\frac{ 1 }{ n }-\frac{ 1 }{ n+2 } for  each integer n≥1. What is the sum of the ﬁrst 20 terms of this sequence?

(A) (1+\frac{ 1 }{ 2 })-\frac{ 1 }{ 20 }
(B) (1+\frac{ 1 }{ 2 })-(\frac{ 1 }{ 21 }-1+\frac{ 1 }{ 22 })
(C) 1-(\frac{ 1 }{ 20 }+\frac{ 1 }{ 22 })
(D) (1-\frac{ 1 }{ 22 }
(E) \frac{ 1 }{ 20 }-\frac{ 1 }{ 22 }

3. { a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 },{ a }_{ n }..
In the sequence above, each term after the ﬁrst term is equal to the preceding term plus the constant c. If { a }_{ 1 }+{ a }_{ 3 }+{ a }_{ 5 }=27, what is the value of { a }_{ 2 }+{ a }_{ 4 }?

4.  In a particular sequence, { S }_{ n } is equal to the units digit of { 3 }^{ n } where n is a positive integer. If { S }_{ 1 }=3, how many of the first 75 terms of the sequence are equal to 9?

5. The sum of the first n terms of an arithmetic series whose nth term is n can be calculated by the formula n(n + 1)/2. Which one of the following equals the sum of the first eight terms in a series whose nth term is 2n ?

A 24
B 48
C 56
D 72 
E 96

6. In the sequence { a }_{ n }, the nth term is defined as { ({ a }_{ n-1 }-1) }^{ 2 }. If { a }_{ 1 }=4, then what is the value of { a }_{ 2 } ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 9

7. The first three terms in an arithmetic sequence are 30, 33, and 36. What is the 80th term?

8. A worker is hired for 7 days. Each day, he is paid 10 dollars more than what he is paid for the preceding day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

(A) 90
(B) 138
(C) 153
(D) 160
(E) 163

9.  Each term of a certain sequence is calculated by adding a particular constant to the previous term. The second term of this sequence is 27 and the fifth term is 84. What is the 1st term of this sequence?

(A) 20
(B) 15
(C) 13
(D) 12
(E) 8

10. In a certain sequence, the term { a }_{ n } is given by the formula { a }_{ n }={ a }_{ n-1 }+5where { a }_{ 1 }=1. What is the sum of the first 75 terms of this sequence?

(A) 10,150
(B) 11,375
(C) 12,500
(D) 13,950
(E) 15,375

11.  A series has three numbers a, ar, and { ar }^{ 2 }. In the series, the first term is twice the second term. What is the ratio of the sum of the first two terms to the sum of the last two terms in the series?

(A) 1:1
(B) 1 : 2
(C) 1 : 4
(D) 2 : 1
(E) 4 : 1

12. The sequence of numbers a, ar, { ar }^{ 2 }, and { ar }^{ 3 } are in geometric progression. The sum of the first four terms in the series is 5 times the sum of first two terms and r\neq -1 and a\neq0. How many times larger is the fourth term than the second term?

(A) 1
(B) 2
(C) 4
(D) 5
(E) 6

13. The sum of the first n terms of a series is 31, and the sum of the first n – 1 terms of the series is 20. What is the value of nth term in the series?

(a) 9
(b) 11
(c) 20
(d) 31 
(e) 51

14. In sequence { A }_{ n }, { A }_{ 1 }= 45 , and { A }_{ n }={ A }_{ n-1 }+2for all integers n > 1. What is the sum of the first 100 terms in sequence { A }_{ n } ?

(A) 243
(B) 14,400
(C) 14,500
(D) 24,300
(E) 24,545

15. The sequence S is defined as { S }_{ n }= 2({ S }_{ n-1 })-4. If { S }_{ 1 }=6, what is { S }_{ 5 }?

(A) -20
(B) 16
(C) 20 
(D) 24 
(E) 36

1 A
2 B
3 18
4 19
5 D
6 E
7 267
8 A
9 E
10 D
11 D
12 C
13 B
14 B
15 E