Different numbers x, y and z are the first three terms of a geometric progression with common ration r, and also the first, second and fourth terms of an arithmetic progression.
a)Find the value of r.
b)Find which term of the arithmetic progression will next be equal to a term of the geometric progression.
solve simulatenously for r=2.
Is the only way to do this to assume that each geometric term is matched with an arithmetic term??
So I must find when x+(n-1)d=xr^3 (if r=2 then d=x)
Solving this for n= 8.
Please let me know if this is fine or if there is a better way.
This is how I solved it . . .Different numbers are the first three terms of a G.P. with common ratio ,
and also the first, second and fourth terms of an A.P.
a) Find the value of
We have: .
Divide  by : .
. . . . . .
We are told that are different numbers, so: .
And we find that: .
The common difference is equal to the first term.
b) Find which term of the A.P. will next be equal to a term of the G.P.
Do we assume that each geometric term is matched with an arithmetic term? . . . . no
The term of the G.P. is: .
The term of the A.P. is: .
They are equal when: .
If , then . . . This is the initial case.
When , then . . .
We can construct a table to display equal terms.