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The number of seats in each row of a theater forms an arithmetic sequence. The fifth row contains 22 seats. The tenth row contains 37 seats . How many seats are in the first row?

2 Answers

2 votes

Let
s_n denote the number of seats in the
n-th row.
s_n is arithmetic, so


s_n=s_(n-1)+d

for some constant
d.

We're told
s_5=22 and
s_(10)=37, so that


s_(10)=s_9+d


s_(10)=(s_8+d)+d=s_8+2d


s_(10)=(s_7+d)+2d=s_7+3d

and so on up to


s_(10)=s_5+5d\implies37=22+5d\implies5d=15\implies d=3

The pattern continues:


s_5=s_4+3


s_5=(s_3+3)+3=s_3+2\cdot3

and so on up to


s_5=s_1+4\cdot3\implies22=s_1+12\implies\boxed{s_1=10}

User Perfection
by
7.6k points
1 vote

Answer:

8

Explanation:

User Kingthorin
by
7.6k points