maths
posted by crystal powell on .
If told that the 3rd term of a GP is 36 and the 8th term is 8748. find the first term and the common ration.

start with 4 with a factor of 3
4 12 36 for the 3rd 
The n  th term of a geometric progression with initial value a and common ratio r is given by:
an = a * r ^ ( n  1 )
In this case :
a3 = a * r ^ ( 3  1 ) = a * r ^ 2 = 36
a8 = a * r ^ ( 8  1 ) = a * r ^ 7 = 8748
So you must solve two equations :
a * r ^ 2 = 36
and
a * r ^ 7 = 8748
a * r ^ 2 = 36 Divide both sides by r ^ 2
a * r ^ 2 / r ^ 2 = 36 / r ^ 2
a = 36 / r ^ 2
a * r ^ 7 = 8748 Divide both sides by r ^ 7
a * r ^ 7 / r ^ 7 = 8748 / r ^ 7
a = 8748 / r ^ 7
a = a
36 / r ^ 2 = 8748 / r ^ 7 Multiply both sides by r ^ 7
36 * r ^ 7 / r ^ 2 = 8748 * r ^ 7 / r ^ 7
36 * r ^ 5 = 8748 Divide both sides by 36
36 * r ^ 5 / 36 = 8748 / 36
r ^ 5 = 243
r = fifth root ( 243 )
r = 3
a = 36 / r ^ 2
a = 36 / 3 ^ 2 = 36 / 9 = 4
OR
a = 8748 / r ^ 7
a = 8748 / 3 ^ 7 = 8748 / 2187 = 4
The first term of a GP:
a = 4
The common ratio:
r = 3