Question

3. If 3, x, y, 18, are in arithmetic progression, (A, P) find the value of x and y

Answer 1

Answer:

Below in bold

Step-by-step explanation:

The sequence is:

3, x, y, 18

If this is an A P then

x - 3 = y - x  

2x - y = 3      (A)  and

y - x = 18 - y

2y - x = 18      (B)

Multiply  (A) by 2:

4x - 2y = 6    (C)

Adding B and C:

3x = 24

x = 8.

and

2y - 8 = 18

2y = 26

y = 13.

So x = 8 and y = 13.

b)   ar + ar^2 = 6ar^3  where a = first term and r = common ratio

Divide by a:

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

r(3r  + 1)(2r  - 1) = 0

So the 2 possible values of r

= -1/3 and 1/2.

i) The common ratio is positive so it must be 1/2.

Second term ar = 8

1/2 a = 8

a = 16.

So the first 6 terms are:

16, 8, 4, 2, 1, 1/2.