In a certain theater, the first row has 12 seats, and each row has 1 m

Question

In a certain theater, the first row has 12 seats, and each row has 1 more seat than the previous row. If the last row has 50 seats, what is the total number of seats in the theater?

A. 1003 
B. 1029 
C. 1129 
D. 1209 
E. 1,339

JeffTargetTestPrep · Accepted Answer

We see that row 1 has 1 + 11 = 12 seats, row 2 has 2 + 11 = 13 seats. Say the last row is row n, and if it has 50 seats, then:

n + 11 = 50

n = 39

So the last row, row 39, has 50 seats.

Now let’s determine the total number of seats in the theater:

sum = average x quantity

sum = (50 + 12)/2 x 39

sum = 31 x 39

sum = 1209

Answer: D

u1983 · Answer

By the given Q-stem this is clearly an AP problem.
Let 's assume there are n rows in the theater. The 1st term=The # seats in the first row = 12; The nth term=The # seats in the nth row =50 & as 'each row has 1 more seat than the previous row', the common difference is d=1
Hence,  50=12+(n-1)*1 
or  38=n-1 
or  n=39 
Hence the total # of seats = the sum of the AP=  (The 1st term+The nth term)*(Total#terms/2) =(39/2)*(12+50)=39*62/2=39*31=1209  
Hence , I would go for  option D .

MathRevolution · Answer

=>

The question asks for the value of 12 + 13 + ... + 50. This is the sum of an arithmetic sequence with first term a = 12, and last term l = 50. 
The sum of n terms of an arithmetic sequence may be found using the formula  \frac{n}{2}  (a + l). 
The number of rows is  n = 50 – 12 + 1 = 39. 
So, the number of seats in the theater is  39 * \frac{( 12 + 50 )}{2} = 39 * \frac{62}{2} = 39 * 31 = 1209.

Therefore, the answer is D.

Answer: D

SSM700plus · Answer

This is an A.P series, every next row has one more seat than previous that of previous row. Difference is d=1

Lets say there are n rows in theater
a=The 1st term=The no of seats in the first row = 12;
an=And nth term=The # seats in the last row =50 
Using the formula an= a +(n-1)d
Hence, 50=12+(n−1)∗1
50=12+(n−1)∗1
50 - 39 = n-1
n = 39
Hence the total number of seats = the sum all the seats in each row = ( 1st term+ nth term)*(Total#terms/2) =(39/2)*(12+50)=39*62/2=39*31=1209

Option Ans -D

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In a certain theater, the first row has 12 seats, and each row has 1 m

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In a certain theater, the first row has 12 seats, and each row has 1 m

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