If the second term of an arithmetic sequence is 5 and the fourth term is 12, what is the 37th term?
2 answers:
By using the information in the question, find a equation in the y=mx+b form. Then, plug in 37 as the x value and solve for y.
Aritmetic sequence
an=a1+d(n-1)
a1=first term
d=common differnce
an=nth term
given
a2=5
a4=12
so
a2=a1+d(2-1)=5
a4=a1+d(4-1)=12
a1+d=5
a1+3d=12
so 12-5=(a1+d)-(a1+3d)=2d=7
2d=7
divide by 2
d=3.5
a2=a1+3.5(1)
5=a1+3.5
minus 3.5 both sides
1.5=a1
an=1.5+3.5(n-1)
37th term
a37=1.5+3.5(37-1)
a37=1.5+3.5(36)
a37=1.5+126
a37=127.5
37th term is 127.5
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Selection B is appropriate.
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It takes 12 times as long to fill the whole tank as it does to fill 1/12 of the tank.
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