Directions: Read each question carefully. Identify what is being asked. Choose the best answer from the four choices
labeled A, B, C, D. Blacken the circle that corresponds to your answer.
1. Which is the first term of an arithmetic sequence if its 5th term is –15 and the 10th term is –30?
A) –5
B) 3
C) 5
D) –3
2. What is the 27th term of the arithmetic sequence: 7, 17, 27, 37…?
A) 207
B) 237
C) 287
D) 307
3. Which term is -99 in the arithmetic sequence: 1, -4, -9, -14, -19…?
A) 15th term
B) 17th term
C) 21st term
D) 25th term
4. There are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third
carriage, and so on in a train. What’s the total number of passengers in the first 7 carriages?
A) 1400
B) 1500
C) 1750
D) 2,025
5. What is the 100th term of the arithmetic sequence: 11, 21, 31, 41…?
A) 891
B)991
C) 1001
D) 1111
6. What are the arithmetic means of the sequence: 140, 166, ____, _____, _____,
A) 172, 208, 280
B) 172, 216, 234
C) 192, 220, 304
D) 192, 218, 244
7. What is the formula for the nth term of the given arithmetic sequence: 3, 7, 11, 15, 18...?
A) An= 4n+1
B) An= 2n+1
C) An= 4n-1
D) An=2n-1
8. What is the sum of the first 25 terms of the sequence -8, 7, … 15n-23…?
A) 4500
B) 5000
C) 5500
D) 6000
9. Which is the 9 term of the geometric sequence –6, 24, –96, 384, . . .?
A) – 1 572 864
B) 1 572 864
C) – 393 216
D) 393 216
10. Which term is 2916 in the geometric sequence 4, 12, 36...?
A) 6
B) 7
C) 8
D) 9
th
th
th
th
11. Which is the first term of the geometric sequence if the fifth term is
th
and the common ratio is 2?
A) 3
B)
C)
D)
12. Which is the geometric mean between –8 and –1 152?
A) 96
B) –96
C) 572
D) –572
13. Which is the sum of the first seven terms in the geometric sequence 9, –45, 225, –1125, . . .?
A) –175 779
B) 175 779
C) –117 189
D) 117 189
14. What is the sum of the first 15 terms of the geometric sequence: 2,4,8, 16, …?
A) 2046
B) 2048
C) 2050
D) 2052
15. What is the geometric mean between 100 and 62, 500?
A) 1000
B) 1500
C) 2500
D) 3000
SEQUECES AND SERIES
1) Which is the 15th term in the arithmetic sequence - 8, - 4, 0, 4, ...?
A) 36
B) 40
C) 44
2) In the arithmetic sequence - 5, -2, 1, 4, ..., which term is 76?
A) 28th
B) 27th
C) 26th
3) Which is the 8th term in the arithmetic sequence 3m + 5n, 4m – n, 5m – 7n, …?
A) 10m – 31n
B) 10m – 37n
C) 11m – 43n
4) Which is the arithmetic mean between – 5 and 23?
A) 18
B) 9
C) – 18
5) Which is the sum of the numbers divisible by 8 from 16 to 160?
A) 1688
B) 1680
C) 1672
6) Which is the 8th term in the geometric sequence 1/2, 3/2, 9/2, ...?
A)
729
2
B)
19683
2
C)
6561
2
7) In the geometric sequence 1/5, 1, 5, 25, ..., which term is 15625?
A) 7th
B) 8th
C) 9th
8) Which is the common ratio in the geometric sequence whose first term is 1/3 and
10th term is 512/3?
A) 4
B) 3
C) 2
9) Which is the geometric mean between 12 and 9?
A) 12
B) 6√3
C) 10.5
10) Which of the pairs of terms are the geometric means of – 3 and – 375?
A) – 15 & 75
B) 15 & –75
C) 15 & 75
D) 48
D) 25th
D) 11m + 43n
D) – 9
D) 1664
D)
2187
2
D) 10th
D) 1
D) 3√6
D) –15 & –75
11) Which is the 7th term in the sequence given by the general term an 
A)
3
7
B)
2
7
C)
n2
?
3n
1
3
D)
12) In the sequence –3, 6, –9, 12, –15..., which is the next term?
A) - 21
B) 15
C) 18
13) In the sequence – 1, 1, –4, –2, –7, …, which term is –8?
A) 5th
B) 6th
C) 7th
14) Which is the sum of the series 2 + (–2) + 2 + (–2) + 2?
A) 2
B) 4
C) –2
15) Which is the 6th term in the sequence given by the general term an 
A)
3
11
B)
3
28
C)
2
3
D) - 18
D) 8th
D) 0
3
?
4(n  1)
1
4
D)
3
7
16) The sequence 1, 1, 2, 3, 5… is called the Fibonacci sequence. Which is the 11th term in the given sequence?
A) 34
B) 55
C) 89
D) 144
17) Which is the sum of the first ten term in the Fibonacci sequence?
A) 140
B) 141
C) 142
D) 143
n 1
18) Which are the first three terms of the sequence given by the general term an  3(2)
?
A) 0, 6, 12
B) 3, 6, 9
C) 3, 6, 12
D) 0, 3, 6
19) Which is the second term in the sequence given by the general term an  7 
A)
27
4
B) 6
C)
20) Which is the next term in the sequence 2, 8, 18, 32…?
A) 44
B) 50
1
?
2n
3
2
D)
C) 60
5
2
D) 64
Directions: Identify the type of sequence of each of the following. Write AS for Arithmetic Sequence, GS
Geometric Sequence, and N for neither arithmetic nor geometric.
1) 29, 23, 17, 11, . . .
6) –3, 3, – 3, 3, . . .
2) – 4, 12, – 36, 108, . . .
7) 34, 3.4, 0.34, 0.034, . . .
3) –19, –11, –3, 5, . . .
8)
4
1
, 2 , , 4, . . .
3
4
4)
1 4 7 10
, , ,
,...
3 3 3 3
9) 1,
5)
1 1
, , 1, 2 , . . .
4 2
10)
1 1
1
,
,
,...
5 25 125
3 6 3 6
, , ,
,...
2 7 5 13
Complete the table applying the formulas for an and Sn.
a1
D
N
3
5
20
8
11
5
–3
10
–4
26
–76
7
–8
an
10
100
Sn
for
A. Matching Type. Match each sequence in column A with its corresponding general term in column
B. (10 pts)
Column A
Column B
5 5
5 5
5
,  , ,  ,…
8 9 10 11 12
A.
_____2) – 1, –3, 7, –11, 15, …
B. an  (1) n1 (4n  5)
_____3) 
5
5 20 25
,…
, 10, ,
,
2
2 13 22
5n
n 3
4n
G. an 
n
an  4n  3
_____1)  ,
F. an 
C. an  n(n  2)
_____4) 7, 11, 15, 19, 23, …
D. an  3n  4n 2
_____5) –1, 0, 3, 8, 15, …
5(1) n
E. an 
n7
B. Match the given summation notation in column A with its corresponding sum in
column B.(10pts)
Column A
Column B
_____ 1)
4
 n(n  4)
_____ 4)
n 2
_____ 2)
5
 3(n  3n 2 )
n 3
_____ 3)
4
 (1)
n2
n
(n  1) n
3
3
 n3
n 1
_____ 5)
4
 3n
2
 5n  4
A.
37
20
D. –7
32
15
B. 54
E.
C. –414
F. 570
n2
2