GRE Sequence Questions (All Possible Q’s to appear on the Exam)

In this post, you will come across all the possible sequence and pattern questions that are likely to appear on the GRE.

by Talha Omer, MBA, M.Eng., Harvard & Cornell Grad

in GRE Quant

In this post, you will come across all the possible sequence and pattern questions that are likely to appear on the GRE.

These are actual real-like GRE questions that you will most likely encounter on the GRE test day.

* Answers can be found at the end of the post.

Questions

Question 1

-2, 6, -18, 54, a, b…

In the sequence of numbers shown, each number after the first is the product of the preceding number and -3.

Quantity A: a

Quantity B: b

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 2

The first term in a certain sequence is 2, and each succeeding term is 4 greater than the previous term. What is the 123rd term in the sequence?

Question 3

\[X=43^{21}–21\]

What is the units digit of X?

Question 4

\[X=29^{31},Y=27^{27}\]

The units digit of X is a and the units digit of Y is b. What is the value of the product ab?

Question 5

\[A=1001^{1001},B=4945^{1001}\]

The tens digit of A is x and the units digit of B is y. What is the value of the sum x+y?

Question 6

R: -4, 4, -4, 4, -4, 4, …

R is a sequence of integers in which -4 and 4 alternate, as shown above. If the average (arithmetic mean) of the first n terms of R is -4/15, what is the value of n?

Question 7

The nth term of a sequence is defined by

\[a_n=(1-2n)^2\]

for all positive integers n.

If the sum of the first p terms is 35, what is the value of p?

Question 8

In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by -2 and then adding 10 to the product. If the fourth term of the sequence is 98, what is the first term of the sequence?

Question 9

In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 2 from the product. If the fifth term of the sequence is 29, then which of the following numbers are in the sequence?

Indicate all that apply.

A) 5

B) 8

C) 9

D) 11

E) 17

F) 53

G) 57

H) 99

Question 10

The first term in a certain sequence is -5, the 2nd term in the sequence is 15, and, for all integers n > 2, the nth term in the sequence is the average (arithmetic mean) of the first n – 1 terms in the sequence. What is the value of the 11th term in the sequence?

Question 11

\[K=439^n\]

where n is a positive integer.

Quantity A: The number of possible values of the units digit of n

Quantity B: 2

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 12

\[X=10^{45}+5\]

When X is divided by 11, the remainder is w.

Quantity A: w

Quantity B: 5

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 13

-4,7,2,-3,1,-4,7,2,-3,1,-4,7,2,-3,1,….

In the sequence above, the first five terms repeat without end. What is the sum of the terms of the sequence from the 127th to the 132nd term?

Question 14

Find the sum of all the integers from -50 to 150, inclusive?

A) 10,050

B) 15,050

C) 15,150

D) 20,100

E) 21,500

Question 15

Quantity A: The sum of the odd integers from -99 to 199, inclusive.

Quantity B: The sum of the even integers from -98 to 198, inclusive.

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 16

X is the decimal form of the fraction 7/11.

Quantity A: The 37th digit to the right of the decimal point in X

Quantity B: 5

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 17

In a sequence of numbers, each term after the first term is equal to the preceding term plus a constant k. If the sum of the first, third, and fifth term of the sequence is 99, what is the sum of the second and the fourth term of the sequence?

Question 18

The nth term of a sequence is defined by

\[a_n=\frac{n}{n+1}\]

for each integer n > 0. What is the product of the first 20 terms of this sequence?

A) 10/21

B) 10/20

C) 1/21

D) 20/21

E) 7/20

Question 19

The first term in a certain sequence is 3, and each succeeding term is one-third of the previous term.

\[\text{Quantity A: The 15th term of the sequence}\\ \text{Quantity B: } 3^{15} \text{ times the 30th term of the sequence}\]

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 20

The first term in a certain sequence is 10/7, and each succeeding term has a numerator of 10 and a denominator that is 1 greater than the denominator of the previous term. Which term of the sequence is equal to the 10th term of the sequence minus the 11th term of the sequence.

Question 21

\[a_1,a_2,a_3,……a_n,…..\]

The nth term of the sequence above is defined as

\[a_n = a_{n-1} + n\]

where n in an integer greater than 2.

\[a_1=2, a_2=4\]

\[\text{Find the value of } a_6?\]

Answers

Q1) B
Q2) 490
Q3) 2
Q4) 27
Q5) 5
Q6) 15
Q7) 23
Q8) -8.5
Q9) A, B, D, E, F
Q10) 5
Q11) C
Q12) B
Q13) 10
Q14) A
Q15) A
Q16) A
Q17) 66
Q18) C
Q19) C
Q20) 266th term
Q21) 22

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GRE Sequence Questions (All Possible Q’s to appear on the Exam)

by Talha Omer, MBA, M.Eng., Harvard & Cornell Grad

in GRE Quant

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