Answer:
D
Step-by-step explanation:
Given:
The sequence is 25, 20, 15, 10, 5.
To find:
The ninth term of the given sequence.
Solution:
We have,
25, 20, 15, 10, 5
It is an AP because the difference between two consecutive terms are same.
Here,
First term (a) = 25
Common difference (d) = 20-25
= -5
The nth terms of an AP is

Where, a is the first term and d is the common difference.
Putting a=25, n=9 and d=-5 to get the 9th term.




Therefore, the ninth term of the given sequence is -15.
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
Answer:
392.1
Step-by-step explanation: just divide and round