Apr 29, 2019 · A geometric sequence has its first term equal to $12$ and its fourth term equal to $-96$. How do I find the common ratio? And find the sum of the first $14$ terms

Oct 17, 2023 · Geometric sequence help, please! How to know if first term is $n=1$ or $n=0$? Ask Question Asked 2 years, 4 months ago Modified 1 year, 10 months ago

Jan 1, 2026 · If I understand right, your question is whether there exists a strictly increasing infinite sequence $\left\ { a_n \right\}$ for which the infinite sequence $\left\ { T_n \right\}$ is a geometric …

Nov 18, 2022 · The comments are mathematically correct that a ratio in a geometric series need not be positive. That said, in the context of a finite geometric series, as is the case here, it would be (at least …

The two are effectively equivalent but the second method views the infinite series as a sequence of partial sums, which is more amenable to proofs and is more rigorous.

I am wondering how to quickly find if a sequence is arithmetic or geometric sequence. for example. an = exp(n) a n = e x p (n) is geometric sequence because

Nov 1, 2016 · A geometric sequence is one that has a common ratio between its elements. For example, the ratio between the first and the second term in the harmonic sequence is $\frac {\frac {1} {2}} …

Sep 20, 2021 · 5 So for, the above formula, how did they get $ (n+1)$ a for the geometric progression when $r = 1$. I also am confused where the negative a comes from in the following sequence of steps.

May 25, 2025 · Do not let the triangle become degenerate. Show that the radii of the inscribed circles are always in a geometric sequence. I made a Geogebra page where you can move the vertex and …

Dec 3, 2016 · For any geometric series, if $|r|<1$, then your series will converge. Your reasoning is perfectly sound. If a series converges, then the limit of its corresponding sequence is zero.