An auditorium has 40 rows. the first row has 20 seats and each row after has 2 additional seats. How many seats are there total?

2 answers:

7 0

This is an arithmetic sequence of the form:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

The sum of an arithmetic sequence is the average of the first and last terms times the number of terms.

s(n)=(a+a+d(n-1))(n/2)

s(n)=(2a+dn-d)(n/2)

s(n)=(2an+dn^2-dn)/2

We are told that the initial term a=20 and that the common difference, d=2 so:

s(n)=(40n+2n^2-2n)/2

s(n)=(2n^2+38n)/2

s(n)=n^2+19n, so for 4o rows the total number of seats will be:

s(40)=40^2+19(40)

s(40)=1600+760

s(40)=2360

Sav [38]3 years ago

5 0

Answer: 20, 22, 24, 26

An arithmetic sequence

a1=20

d=2

98 seats

an arithamtic series

2,360 total seats

Step-by-step explanation:

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