An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Question

nnesha · Answer

$$a_1 = 10 ~~~~a_2 =12$$
do you know the common difference ?

nnesha · Answer

it's Arithmetic seq
bec 
first one is 10
then 2nd one is 12
3rd one is 14

nnesha · Answer

do you know the formula ??

aaronandyson · Answer

Formula for the sum of arithmetic sequence is
Sn = (n/2) (A1 + An)
where A1 is the first and An is the last term.
In our case, sequence has 20 terms (20 rows in auditorium) and the last term (= number of seats in 20th row) is
A20 = 2(20 + 4) = 48
now the sum is
S20 = (20/2) (10 + 48) = 10 * 58 = 580