Random question I came across when studying, couldn't work out how to do it.
Question:
The first three terms of a gemoetric sequence are x^2 - 1, 5x - 1 and -3. Find all possible values of a, the first term and r, the common ratio.
Thanks.
recall that in a geometric progression, the nth term, , is given by:
for
thus, since the first term is it means that
also, the second term is:
...................(1)
the third term is:
..................(2)
Now, equate (1) and (2), we get:
now solve that to et a range of values for , and then you can find the possible values for and
EDIT: Ah, Jan's way is easier