Answer:
7
Step-by-step explanation:
F(x)=3x +1
F(2) = 3(2) +1
F(2)= 6 +1
F(2) = 7
F(x)=7
Let a, b and c be in a geometric sequence, then ac = b^2
Hence, (2k + 1)(7k + 6) = (3k + 4)^2
14k^2 + 19k + 6 = 9k^2 + 24k + 16
5k^2 - 5k - 10 = 0
5k^2 + 5k - 10k - 10 = 0
5k(k + 1) - 10(k + 1) = 0
(5k - 10)(k + 1) = 0
5k - 10 = 0 or k + 1 = 0
5k = 10 or k = -1
k = 2 or k = -1
The geometric sequence formed is
2(2) + 1, 3(2) + 4, and 7(2) + 6
5, 10, and 20
OR
2(-1) + 1, 3(-1) + 4, and 7(-1) + 6
-1, 1, and -1
We can write a system of equations.
x + y = 77
y = x + 5
Plug in x + 5 into the first equation:
x + y = 77
x + (x + 5) = 77
So this is our answer.
6/11 = 0.54_54 . . . . . the digits 54 are repeated indefinitely
You can arrive at the digits 54 by multiplying the numerator (6) by 9. This will be the case for any proper fraction with 11 as a denominator.
