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:
Angle M = 120 degrees
Shortest side = MN
Middle Side = MO
Longest side = ON
Step-by-step explanation:
Answer:
810 boys
Step-by-step explanation:
1800 students and 55% are girls.
100%-55%=45%
1800*0.45 = 810
1800*0.55 = 990
So there are 990 girls and 810 boys.
Hope this helps :)
The simplest solution is:
2452 = 60q +52r
2452 = 60q + 52(1)
2452 -52 = 60q
2400 = 60q
2400/60 =q
40 = q
r = 1: q = 40
Jessica's annual salary is $68571.43.
Data;
- percentage saved for housing = 28%
- amount saved annually = $1600
<h3>Percentage</h3>
This is the ratio of a number to the entire value and multiplied by 100
The percentage set aside for housing is given as 28% which is $1600.
Let find 28% of x which is equal to 1600
cross multiply both sides and solve for x
Divide both sides by the coefficient of x
Her monthly income is $5714.28.
Let's multiply this by 12 (months in a year) to determine her gross monthly income.
From the above calculations, Jessica's annual salary is $68571.43.
Learn more on percentage here;
brainly.com/question/25567167
