Originally Posted by

**woollybull** 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.

a)

y=xr, z=xr^2

y=x+d,

z=x+3d

xr =x+d,

xr^2=x+3d

solve simulatenously for r=2.

b)

**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.

Thanks.