Answer:
<h3>The nth term
Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequences</h3>
Step-by-step explanation:
Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.
If the sum of the first two term is 24, then a/r + a = 24...(1)
and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)
Substtituting equation 1 into 2 we have;
24+ar = 26
ar = 2
a = 2/r ...(3)
Substituting a = 2/r into equation 1 will give;
(2/r))/r+2/r = 24
2/r²+2/r = 24
(2+2r)/r² = 24
2+2r = 24r²
1+r = 12r²
12r²-r-1 = 0
12r²-4r+3r -1 = 0
4r(3r-1)+1(3r-1) = 0
(4r+1)(3r-1) = 0
r = -1/4 0r 1/3
Since a= 2/r then a = 2/(-1/4)or a = 2/(1/3)
a = -8 or 6
All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of a geometric sequence is expressed as
if r = -1/4 and a = -8
Tn = -8(-1/4)^(n-1)
if r = 1/3 and a = 6
Tn = 6(1/3)^(n-1)
The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms
Answer:
B can be 1, 2, 4, 7, 8, 14, 28 and 56.
Basically any factor of 56.
Hope that helps!
<em>-scsb17hm</em>
Step-by-step explanation:
Answer:
y=5/7 x=31/7
Step-by-step explanation:
Make the x values the opposite of each other:
-2(x+5y=8)
-2x-10y=-16
2x+3y=9
Combine like terms and solve for y:
-7y=-5
y=5/7
Plug y in to find x.
x+5(5/7)=8
x+25/7=8
56/7-25/7=x
x=31/7
(length of tree's shadow)/(height of tree) = (length of person's shadow)/(person's height)
24/x = 8/5
24*5 = x*8
120 = 8x
8x = 120
8x/8 = 120/8
x = 15
The tree is 15 feet tall
7/3 IS an improper fraction 2 1/3 is a mixed number
