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:
See below ↓↓
Step-by-step explanation:
<u>Plan 1</u>
<u>Plan 2</u>
<u>Part A</u>
<u>Equating them</u>
⇒ 127x = 363 + 94x
⇒ 33x = 363
⇒ x = <u>11 months [They will be same at this point]</u>
<u>Part B</u>
⇒ Plan 1 : 127(24) = $3048
⇒ Plan 2 : 363 + 94(24) = 2256 + 363 = $2619
⇒ I would recommend Plan 2 as it costs less for the time period of 2 years
well if 6 is half of 12 im sure 60 is half of 120 so A
Answer:
Step-by-step explanation:
<em>Vertical angles are equal as per definition.</em>
- ∠E and ∠F are vertical angles
- m∠E = 9x+12 and m∠F = 3x+24
- x = ?
<u>Solution</u>
- 9x+12 = 3x+24
- 9x - 3x = 24 - 12
- 6x = 12
- x = 2
