The first three terms of an arithmetic sequence, a, a+d and a + 2d, are the same as the first three terms, a, ar, ar^2, of a geometric sequence ( a does not equal 0).
Show that this is only possible if r=1 and d=0

I am not sure how they want me to prove this.

Question

The first three terms of an arithmetic sequence, a, a+d and a + 2d, are the same as the first three terms, a, ar, ar^2, of a geometric sequence ( a does not equal 0).
Show that this is only possible if r=1 and d=0

I am not sure how they want me to prove this.

koikkara · Answer

@imqwerty this user might help you. @Zas

anonymous · Answer

Thanks!

imqwerty · Answer

the sum of 1st 3 terms of AP1st term of both the series is a
so its clear that 
a=a :D

now we come to the second term$$a+d=ar$$
$$d=ar-a=>d=a(r-1)$$
nd the third terms are also equal so $$a+2d=ar^2$$
put d=a(r-1) in this eq.
$$a+2a(r-1)=ar^2$$divide the whole equation by a u get-$$1+2(r-1)=r^2   =>r^2  -2r+1=0 =>(r-1)^2=0$$so r =1

put r=1  in 
d=a(r-1)
d=a(1-1)
d=0

imqwerty · Answer

hey forget that 1st line i forgot to delete that 
instead of that it must be-
1st terms of both series r same so 
a=a

anonymous · Answer

Ok, thank you very much!