A new movie theater has stadium seating. The first row has 10 seats. Each additional row has 4 seats more than the row before it. How many seats are in the theater if there are 16 rows of seats?

Question

anonymous · Answer

Formula for partial sums
Sn=n/2*(a1+an)
a1=10
an=10+4(16-1)=70
n=16
Sn=(16/2)*(10+70)
=80*8=640

campbell_st · Answer

this is an arithmetic sequence 

10, 14, 18, ... 

so to find the number of seats use 

$$S_{n} = \frac{n}{2}[2a + (n - 1)\times d]$$

a is the 1st term in the sequence, n is the number of terms and d is the common difference. 

In your question you have a = 10, d = 4 and n = 16 

substitute and then evaluate, and you'll have the number of seats in the theatre