Solve for x by simplifying both sides of the equation then isolating teh varible.
your answer = - 1/7
Sequence: 5/2, 5/4, 5/8, 5/16
a8=?
a1=5/2
a2=5/4
a3=5/8
a4=5/16
a2/a1=(5/4)/(5/2)=(5/4)*(2/5)=(5*2)/(4*5)=2/4=1/2
a3/a2=(5/8)/(5/4)=(5/8)*(4/5)=(5*4)/(8*5)=4/8=1/2
a4/a3=(5/16)/(5/8)=(5/16)*(8/5)=(5*8)/(16*5)=8/16=1/2
Ratio: r=a2/a1=a3/a2=a4/a3→r=1/2
an=a1*r^(n-1)
a1=5/2, r=1/2
an=(5/2)*(1/2)^(n-1)
an=(5/2)*[1^(n-1)/2^(n-1)]
an=(5/2)*[1/2^(n-1)]
an=(5*1)/[2*2^(n-1)]
an=5/2^(1+n-1)
an=5/2^n
n=8→a8=5/2^8
a8=5/256
Answers:
The formula for the general term or nth term for the sequence is an=5/2^n
a8=5/256
2r + 2s = 50
2r - s = 17
-----------subtract
3s = 33
s = 11
2r - s = 17
2r - 11 = 17
2r = 28
r = 14
so r = 14 and s = 11
answer is C. r = 14, s = 11
2 divided by 1/2
2 x 2/1 = 4
3/4 x 4/1 = 12/3
12/3 = 4
4 gallons, Hope this helps!