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.
Divide it into chunks of area you can find. One way to divide it is
.. a rectangle 2 mi x 5 mi at upper left.
.. a rectangle 8 mi x 6 mi down the middle
.. a rectangle 3 mi x 4 mi at lower right
.. a triangle 5 mi x 6 mi at lower left
Then the sum of areas is
.. (2 mi)*(5 mi) +(8 mi)*(6 mi) +(3 mi)*(4 mi) + (1/2)*(5 mi)*(6 mi)
.. = 10 mi^2 +48 mi^2 +12 mi^2 +15 mi^2
.. = 85 mi^2
Y=4 on the first one
A=92 on the second one
So 1/8 per month
1/8 * 12 months = 3/2
Reduced is 1 1/2 inches per year
