Geometric sequence has first term $a$ and last term $l$ and the sum of all these terms is $S$. Prove that the common ratio of the sequence is $\frac{S-a}{S-l}$.
How to include the answer with $S$?
Geometric Progression prove the answer
0
$\begingroup$
arithmetic-geometry
geometric-progressions
1 Answers
1
Hint:
$$l=ar^{n-1}$$ $$ar^n=lr$$
Subsitute the above equation into $$S=\frac{a(r^n-1)}{r-1}$$
We obtain
$$S=\frac{lr-a}{r-1}$$
Solve for $r$