Question
Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}, \ldots$ be a geometric sequence. Find each of the indicated quantities.$$a_{1}=1, a_{4}=-1 ; a_{100}=?$$
Step 1
We know that in a geometric sequence, the ratio of any two consecutive terms is constant. This ratio is given by $a_{n+1}/a_{n}$. So, we can find the common ratio $r$ by dividing $a_{4}$ by $a_{1}$: $$r = \frac{a_{4}}{a_{1}} = \frac{-1}{1} = -1.$$ Show more…
Show all steps
Your feedback will help us improve your experience
Babita Kumari and 75 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}, \ldots$ be a geometric sequence. Find each of the indicated quantities. $$ a_{1}=-1, a_{8}=1 ; a_{99}=? $$
Sequences, Induction, and Probability
Arithmetic and Geometric Sequences
Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}, \ldots$ be a geometric sequence. Find each of the indicated quantities. $$ a_{1}=9, r=\frac{2}{3} ; S_{10}=? $$
Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}, \ldots$ be a geometric sequence. Find each of the indicated quantities. $$ a_{1}=8, a_{2}=2 ; r=? $$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD