pretty much completely lost on this question even after reading the explanation

Q:Sequence A is defined by the equation An = 3n + 7, where n is an integer greater than or equal to 1. If set B is comprised of the first x terms of sequence A, what is the median of set B ?

(1) The sum of the terms in set B is 275.

(2) The range of the terms in set B is 30.


The answers imply that the set begins with n=1

thus the first term = 10 (3(1)+7), the second term, n=2, =13 (3(2) +7).

for statement 1 I understand that if we know the sum & the number of terms we know median & mean but I get lost on the rest. Beginning with why are we starting with n = 1. Where is this stated in the question?

I read Set b has the first X number of terms but why for example wouldn't the sequence start with n = 5?

I have an added question to the same topic.

How do you solve the first statement?

Sum of terms in set B is 275.

275 =(10 + 3n+7)/2)*n

Are we supposed to solve to find out the roots or assume that it can be solved?

Hi Jeremy,

Just see the first line where it is written that sequence is given as
3n + 7, where n is an integer greater than or equal to 1

So minimum value of n is 1.

when n=1, sequence term is 10
when n=2, sequence term is 13
when n=3, sequence term is 16

The language is a bit complicated but finally if you see the sequence it is simply:

10, 13, 16, 19, 22 .........and so on

So it is an AP with first term as 10 and common difference as 3.


Now set B is comprised of the first x terms of sequence A.

so b= {10, 13, 16,......x terms}


We have to find Median of set B.


The question is basically checking whether we can find out x?

By applying Sum formula of AP we can find out x

(x/2)x{(2x10) + (x-1) x 3} = 275.

This will result in a quadratic equation in x

3x^2+17x-550 = 0

x comes as 11.

So we know that 6th term will be the median hence sufficient

Now St. 2

The range of the terms in set B is 30.

Again here we have to find x.

Range of a set = (Highest value - Lowest value)


for set B, Range : (Xth term - 10)

By formula:

L=a+(x-1).d .....for an AP, where L is the xth term, a is the first term, and d common difference

L-a is given as 30, d = 3

so x is known.

Thus sufficient.

Ans. will be D

In my opinion you have to see whether real roots exist. Fortunately, perfect squares come and also out of two values, only one is an integer.

So yeah, to the original question, we are told that n values are 1 and up AND we are told to take the first few terms of the sequence. These things together indicate to us that we are indeed to start at n=1..

For solving the quadratic, if you're really used to this type of problem, you will notice that by its nature the formula must produce equations with unique positive integer answers (unless the question is rendered invalid by an invalid sum). BUT you don't have to notice that, it's just a shortcut. You can always solve for n if you want and be sure.. :)

_________________
Tim Sanders
Manhattan GMAT Instructor