1955 AHSME Problems/Problem 45
Problem 45
Given a geometric sequence with the first term and
and an arithmetic sequence with the first term
.
A third sequence
is formed by adding corresponding terms of the two given sequences.
The sum of the first ten terms of the third sequence is:
Solution
Let our geometric sequence be and let our arithmetic sequence be
. We know that
This implies that
, hence
and
. We can rewrite
as
plugging this into
we get
r(r-2)=0
r=0
2
r\neq 0
r=2
d=-1
\{1-n\}
\{2^{n-1}\}
\fbox{A}$.