What is the 57th term of the GP (geometric progression) whose first te

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GMATBusters’ Quant Quiz Question -6

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What is the 57th term of the GP (geometric progression) whose first term is 5?

(1) The second term of the sequence = 10
(2) The third term of the sequence = 20

GMATBusters · Answer

Official Solution:

What is the 57th term of the GP (geometric progression) whose first term is 5?
GP : a, ar, a r^2 
a = 5, hence the terms are 5, 5r, 5 r^2

(1) The second term of the sequence = 10
5r = 10, so r = 2.
Hence, 57th term = ar^56 can be found out
Sufficient

(2) The third term of the sequence = 20
5 r^2  = 20
 r^2  = 4
r = +/-2 ,
Hence, 57th term = ar^56 can be found out.
Sufficient

Answer D

Raxit85 · Answer

What is the 57th term of the GP (geometric progression) whose first term is 5?
first term = 5, we need the ratio to calculate GP
1) The second term of the sequence = 10, 
We can get ratio and we know first term. So sufficient. we don't need to calculate the exact no. but we'll get unique one.

2) The third term of the sequence = 20
Not sufficient as we can't get the ratio (as we don't know the second no.)

Ans. A

ashwini2k6jha · Answer

tn= ar^56
state1:ar=10given a=5
r=2,ar^56=5*2^56 sufficient
State2:ar^2=20,r=+-2
5*2^56
sufficient 
Answer D

Archit3110 · Answer

since terms are in GP i.e a common ratio
given 1st term = 5
#1
 The second term of the sequence = 10
10= 5 * r^1
r= 2
57th term
t57 = 5 * (2)^56
sufficient
#2
The third term of the sequence = 20
t3 = t1 * r^2
20= 5 *r^2
r= +/-2
insufficient
OPTION A

What is the 57th term of the GP (geometric progression) whose first term is 5?
1) The second term of the sequence = 10
2) The third term of the sequence = 20

uc26 · Answer

Since we are given that the given progression is a geometric progression, we need to know the common ratio in the progression to be able to find the 57th term.

1) Since we have two terms , we can find the common ratio i.e. 2nd term/ 1st term= 10/5= 2. Sufficient.
2) Since we have the 1st and 3rd term of the progression, we can find that the common ratio should be 2. Even though we do not have the 2nd term, we know that the said progression is a geometric progression with a common ratio and the only way to get from 5 to 20 is multiplying it by a 4= 2*2. Thus the common ratio would be 2. Sufficient.
Answer: D

Kinshook · Answer

Asked: What is the 57th term of the GP (geometric progression) whose first term is 5?
In a GP nth term = t_n = 5*r^{n-1}; where r is common ratio

1) The second term of the sequence = 10
 t_2 = 5*r = 10 
 r=\frac{10}{5} =2 
 t_{57}=5*2^{56} 
SUFFICIENT

2) The third term of the sequence = 20 
 t_3 = 5*r^2 = 20 
 r^2 = \frac{20}{5} = 4 
 t_{57} = 5*r^{56} = 5*4^{28} = 5*2^{56} 
SUFFICIENT

IMO D

DAraYnpMM8M

1BlackDiamond1 · Answer

The answer is E.

Statement 1 is not sufficient to answer the question.
Statement 2 is not sufficient to answer the question.
TOgether not sufficient to answer the question

freedom128 · Answer

Q. What is the 57th term  (a57)  of the GP (geometric progression) whose first term  (a1)  is 5?

an = a1 * r^(n-1)
where: an is the n-th term of GP and r is the ratio

(1) The second term of the sequence (a2) = 10

a2 = a1 * r^(2-1)
10 = 5 * r 
r=2

We know a1 and r. Thus, we can calculate a57 = a1 * r^56 = 5* 2^56. 
SUFFICIENT

(2) The third term of the sequence (a3) = 20

a3 = a1 * r^(3-1)
20 = 5 * r^2
r=2

We know a1 and r. Thus, we can calculate a57 = a1 * r^56 = 5* 2^56. 
SUFFICIENT

FINAL ANSWER IS (D)

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StevenA · Answer

What is the 57th term of the GP (geometric progression) whose first term is 5?
1) The second term of the sequence = 10
2) The third term of the sequence = 20

Let's assess the first statement.
 a_n = a r^{n-1} 
 a_2 = 10 = 5 r^{1} . r = 2

Let's assess the second statement.
 a_n = a r^{n-1} 
 a_3 = 20 = 5 r^{2} . 
 r^{2} = 4  .
Here, r may be 2 or r may be -2. Hence, it is not sufficient.

The answer is A (only statement 1)

shameekv1989 · Answer

a_n = a_1 * r^{n-1}

i)  a_1 = 5

a_2 = a_1 * r  =>  10 = 5*r  => r=2 - Sufficient

ii)  a_3 = a_1 * r^2  =>  20 = 5*r^2  => r = +-2 - Insufficient

Answer - A

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