Answer:
Part 15) The next three terms are 5/8,3/4 and 7/8
Part 16) The 37th term is -35.5
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant and this constant is called the common difference (d)
Part 15) Find the next three terms of the arithmetic sequence
[tex]\frac{1}{8},\frac{1}{4},\frac{3}{8},\frac{1}{2},...[/tex]
so
[tex]a1=1/8\\ a2=1/4\\ a3=3/8\\ a4=1/2\\ a2-a1=1/4-1/8=1/8\\ a3-a2=3/8-1/4=1/8\\ a4=a3=1/2-3/8=1/8[/tex]
The common difference is equal to
d=1/8
Find the next three terms of the arithmetic sequence
Find a5
[tex]a5=a4+d[/tex] ----->[tex]a5=1/2+1/8=5/8[/tex]
Find a6
[tex]a6=a5+d[/tex] ----->[tex]a6=5/8+1/8=3/4[/tex]
Find a7
[tex]a7=a6+d[/tex] ----->[tex]a7=3/4+1/8=7/8[/tex]
therefore
The next three terms are
5/8,3/4 and 7/8
Part 16) what is the 37th term of the arithmetic sequence
[tex]4.1,3,1.9,0.8,...?[/tex]
so
[tex]a1=4.1\\ a2=3\\ a3=1.9\\ a4=0.8[/tex]
[tex]a2-a1=3-4.1=-1.1\\ a3-a2=1.9-3=-1.1\\ a4=a3=0.8-1.9=-1.1[/tex]
The common difference is equal to
d=-1.1
We can write an Arithmetic Sequence as a rule
[tex]an=a1+d(n-1)[/tex]
substitute the values
[tex]an=4.1-1.1(n-1)[/tex]
For n=37
substitute
[tex]a37=4.1-1.1(37-1)[/tex]
[tex]a37=4.1-1.1(36)[/tex]
[tex]a37=-35.5[/tex]
