If a = first term and r = common ratio we have
a + ar + ar^2 = 13 and ar^2 / a = r^2 = 9
so r = 3
and a + 3a + 9a = 13
so a = 1
so they are 1,3 and 9
2.
in geometric series we have
4 , 4r ,4r^2 , 60
Arithmetic;
4, 4r , 4r + d , 4r + 2d
so we have the system of equations
4r + 2d = 60
4r^2 = 4r + d
From first equation
2r + d = 30
so d = 30 - 2r
Substitute for d in second equation:-
4r^2 - 4r - (30-2r) = 0
4r^2 - 2r - 30 =0
2r^2 - r - 15 = 0
(r - 3)(2r + 5) = 0
r = 3 or -2.5
r must be positive so its = 3
and d = 30 - 2(3) = 24
and the numbers are 4*3 = 12 , 4*3^2 = 36
first 3 are 4 , 12 and 36 ( in geometric)
and last 3 are 12, 36 and 60 ( in arithmetic)
The 2 numbers we ause are 12 and 36.
The nth term of the sequence is 2n - 8
<h3>Equation of a function</h3>
The nth term of an arithmetic progression is expressed as;
Tn = a + (n - 1)d
where
a is the first term
d is the common difference
n is the number of terms
Given the following parameters
a = f(1)=−6
f(2) = −4
Determine the common difference
d = f(2) - f(1)
d = -4 - (-6)
d = -4 + 6
d = 2
Determine the nth term of the sequence
Tn = -6 + (n -1)(2)
Tn = -6+2n-2
Tn = 2n - 8
Hence the nth term of the sequence is 2n - 8
Learn more on nth term of an AP here: brainly.com/question/19296260
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The question is a bit ambiguous: you may mean
or
Anyway, in both cases, the domain of a function involving a square root is found by imposing the content of the root to be greateer than or equal to zero. So, in the first case you have
In the second case, you have
Rectangular and polar forms are two forms of equations that translates to plot. In this case, the two forms are convertible to each other by the expressions:
r sin theta = y
r cos theta = x
x2 + y2 = r2
we are given the polar expression r csc theta = 8 and is asked to convert to rectangular form.
in this case, csc theta is equal to 1/ sin theta. thys
r / sin theta = 8
in order to make use of the equations above, then
we multiply r to both numerator and denominator in the left side, that is
r^2 / r sin theta = 8
x2+y2 / y = 8
x 2 + y2 = 8y
A = Andrew
S = Sister
A : S
2 : 3
2 + 3 = 5
250 ÷ 5 = 50
2 × 50 = 100
3 × 50 = 150
∴ A : S
100 : 150
So Andrew keeps £100 of his salary every week.
Of this, he saves 12%:
100 × (12 ÷ 100) = 12
So he saves £12 every week
360 ÷ 12 = 30
∴ it will take him 30 weeks to save £360.
