1.
| Quantity A | Quantity B |
| The sum of the odd integers from [latex]1[latex] to [latex]199[latex] | The sum of the even integers from [latex]2[latex] to [latex]198[latex] |
2. The sequence of numbers [latex]{ a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 }[latex]… [latex]{ a }_{ n }[latex].. is defined by [latex]{ a }_{ n }=\frac{ 1 }{ n }-\frac{ 1 }{ n+2 }[latex] for each integer [latex]n[latex]≥[latex]1[latex]. What is the sum of the first 20 terms of this sequence?
(A) [latex](1+\frac{ 1 }{ 2 })-\frac{ 1 }{ 20 }[latex]
(B) [latex](1+\frac{ 1 }{ 2 })-(\frac{ 1 }{ 21 }-1+\frac{ 1 }{ 22 })[latex]
(C) [latex]1-(\frac{ 1 }{ 20 }+\frac{ 1 }{ 22 })[latex]
(D) [latex](1-\frac{ 1 }{ 22 }[latex]
(E) [latex]\frac{ 1 }{ 20 }-\frac{ 1 }{ 22 }[latex]
3. [latex]{ a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 },{ a }_{ n }[latex]..
In the sequence above, each term after the first term is equal to the preceding term plus the constant [latex]c[latex]. If [latex]{ a }_{ 1 }+{ a }_{ 3 }+{ a }_{ 5 }=27[latex], what is the value of [latex]{ a }_{ 2 }+{ a }_{ 4 }[latex]?
4. In a particular sequence, [latex]{ S }_{ n }[latex] is equal to the units digit of [latex]{ 3 }^{ n }[latex] where [latex]n[latex] is a positive integer. If [latex]{ S }_{ 1 }=3[latex], how many of the first [latex]75[latex] terms of the sequence are equal to [latex]9[latex]?
5. The sum of the first [latex]n[latex] terms of an arithmetic series whose nth term is [latex]n[latex] can be calculated by the formula [latex]n(n + 1)/2[latex]. Which one of the following equals the sum of the first eight terms in a series whose [latex]n[latex]th term is [latex]2n[latex] ?
A [latex]24[latex]
B [latex]48[latex]
C [latex]56[latex]
D [latex]72[latex]
E [latex]96[latex]
6. In the sequence [latex]{ a }_{ n }[latex], the nth term is defined as [latex]{ ({ a }_{ n-1 }-1) }^{ 2 }[latex]. If [latex]{ a }_{ 1 }=4[latex], then what is the value of [latex]{ a }_{ 2 }[latex] ?
(A) [latex]2[latex]
(B) [latex]3[latex]
(C) [latex]4[latex]
(D) [latex]5[latex]
(E) [latex]9[latex]
7. The first three terms in an arithmetic sequence are [latex]30, 33[latex], and [latex]36[latex]. What is the [latex]80[latex]th term?
8. A worker is hired for [latex]7[latex] days. Each day, he is paid [latex]10[latex] dollars more than what he is paid for the preceding day of work. The total amount he was paid in the first [latex]4[latex] days of work equaled the total amount he was paid in the last [latex]3[latex] days. What was his starting pay?
(A) [latex]90[latex]
(B) [latex]138[latex]
(C) [latex]153[latex]
(D) [latex]160[latex]
(E) [latex]163[latex]
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 [latex]27[latex] and the fifth term is [latex]84[latex]. What is the 1st term of this sequence?
(A) [latex]20[latex]
(B) [latex]15[latex]
(C) [latex]13[latex]
(D) [latex]12[latex]
(E) [latex]8[latex]
10. In a certain sequence, the term [latex]{ a }_{ n }[latex] is given by the formula [latex]{ a }_{ n }={ a }_{ n-1 }+5[latex]where [latex]{ a }_{ 1 }=1[latex]. What is the sum of the first [latex]75[latex] terms of this sequence?
(A) [latex]10,150[latex]
(B) [latex]11,375[latex]
(C) [latex]12,500[latex]
(D) [latex]13,950[latex]
(E) [latex]15,375[latex]
11. A series has three numbers [latex]a[latex], [latex]ar[latex], and [latex]{ ar }^{ 2 }[latex]. 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) [latex]1:1[latex]
(B) [latex]1 : 2[latex]
(C) [latex]1 : 4[latex]
(D) [latex]2 : 1[latex]
(E) [latex]4 : 1[latex]
12. The sequence of numbers [latex]a[latex], [latex]ar[latex], [latex]{ ar }^{ 2 }[latex], and [latex]{ ar }^{ 3 }[latex] are in geometric progression. The sum of the first four terms in the series is [latex]5[latex] times the sum of first two terms and [latex]r\neq -1[latex] and [latex]a\neq0[latex]. How many times larger is the fourth term than the second term?
(A) [latex]1[latex]
(B) [latex]2[latex]
(C) [latex]4[latex]
(D) [latex]5[latex]
(E) [latex]6[latex]
13. The sum of the first [latex]n[latex] terms of a series is [latex]31[latex], and the sum of the first [latex]n – 1[latex] terms of the series is [latex]20[latex]. What is the value of [latex]n[latex]th term in the series?
(a) [latex]9[latex]
(b) [latex]11[latex]
(c) [latex]20[latex]
(d) [latex]31[latex]
(e) [latex]51[latex]
14. In sequence [latex]{ A }_{ n }[latex], [latex]{ A }_{ 1 }= 45[latex] , and [latex]{ A }_{ n }={ A }_{ n-1 }+2[latex]for all integers [latex]n > 1[latex]. What is the sum of the first [latex]100[latex] terms in sequence [latex]{ A }_{ n }[latex] ?
(A) [latex]243[latex]
(B) [latex]14,400[latex]
(C) [latex]14,500[latex]
(D) [latex]24,300[latex]
(E) [latex]24,545[latex]
15. The sequence [latex]S[latex] is defined as [latex]{ S }_{ n }= 2({ S }_{ n-1 })-4[latex]. If [latex]{ S }_{ 1 }=6[latex], what is [latex]{ S }_{ 5 }[latex]?
(A) [latex]-20[latex]
(B) [latex]16[latex]
(C) [latex]20[latex]
(D) [latex]24[latex]
(E) [latex]36[latex]
Answer:
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
