if a b 9 are in GP
b÷a = 9 ÷ b
b^2 = 9a
if a - 1 b 9 are in AP
2b = a+8
b = a+8÷2
substitute
b is equal to a + 8 by 2 in b square equal to 9 a
(a+8÷2)^2 = 9a
a^2+16a+64 = 36a
a^2 -20a +64 =0
(a-16) (a-4) =0
a= 16 or a=4
when a=16 b= 12
when a=4 b= 6
Value of a and b are given above
Given:
Joining fee = $28
Fee of each event = $4
To find:
Total cost for someone to attend 4 events.
Solution:
Let the number of events be x and total fee be y.
Fee for 1 event = $4
Fee for x events = $4x
Joining fee remains constant. So, the total fee is

Substitute x=4 in this equation.



Therefore, total cost of 4 events is $44.