The fourth term of a Geometric Progression is 48 and the sixth term is 12. Find the possible values of the common ratio and the corresponding values of the first term.

Common ratio = 1/2 and first term = 384

or common ratio = -1/2 and first term = -384.

Step-by-step explanation:

T6/T4 = r^5 / r^3  where r = the common ratio and T6 and T4 are 6th and 4th terms

r^5 / r^3 = 12/48

r^2 = 1/4

so r = +/- 1/2.

The 4th term = a r^3  where a = first term.

If r = 1/2:-

48 = a *(1/2)^3 = a/8  

a = 8*48

= 384.

if r = -1/2,  then a = -384

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180

the answer is 5636.7