Question 898852
you are given that:


the sum of the 2d and 3d terms is 9.


the 7th term is 8 times the 4th.


in a geometric progression, the formula for An is:


An = A1 * r^(n-1)


This means that A7 = A1 * r^6


This means that A4 = A1 * r^3


if A7 is 8 * A4, this means that:


A1 * r^6 = 8 * A1 * r^3


divide both sides of this equation by A1 * r^3 and you get:


(A1 * r^6) / (A1 * r^3) = 3


simplify to get:


r^3 = 8 which results in r = 2.


you know  that A2 = A1 * r


you also know that A3 = A1 * r^2


since r = 2, this becomes:


A2 = A1 * 2


A3 = A1 * 4


the sum of A2 and A3 is equal to 6 * A1 which is equal to 9


this means that A1 must be equal to 3/2


since A1 is equal to 3/2 and r is equal to 2, this means that A5 is equal to A1 * r^4 which is equal to 3/2 * 2^4) which is equal to 3/2 * 16 which is equal to 24.


the progression from A1 to A7 is as follows:


A1 = 3/2
A2 = 3/2 * 2 = 3
A3 = 3/2 * 4 = 6
A4 = 3/2 * 8 = 12
A5 = 3/2 * 16 = 24
A6 = 3/2 * 32 = 48
A7 = 3/2 * 64 = 96


the sum of the second and third term is equal to 9 because 3 + 6 = 9
the 7th term is 8 times the 4th term because 8 * 12 = 96


your solution is:



first term is equal to 3/2
ratio is equal to 2
fifth term is equal to 24.