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Rus_ich [418]
3 years ago
8

The number of seats in each row of a theater forms an arithmetic sequence. The fifth row contains 22 seats. The tenth row contai

ns 37 seats . How many seats are in the first row?
Mathematics
2 answers:
babymother [125]3 years ago
8 0

Answer:

8

Step-by-step explanation:

beks73 [17]3 years ago
7 0

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}

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