SL 1.8—Sum of infinite geo sequence Questionbank

A geometric progression has a fourth term of 8 and a sum to infinity which is four times the first term.

The second term of a geometric progression is $24$ and the sum to infinity is $128$.

A geometric progression has first term $2$ and common ratio $r$. A second geometric progression has first term $6$ and common ratio $\frac{1}{3}r$. The two progressions have the same sum to infinity, $S$.

A geometric progression, in which all the terms are positive, has a common ratio $r$. The sum of the first $n$ terms is less than $80\%$ of the sum to infinity.

The second term of a geometric progression is $12$ and its fourth term is $\frac{27}{4}$. Given that the common ratio is positive,

The first, second and third terms of a geometric progression are $m + 1$, $2m + 6$, and $4m + 24$ respectively, where $m$ is a positive whole number.

In a geometric progression, the sum to infinity is equal to five times the first term.

The first two terms of an infinite geometric sequence are $v_1 = 18$ and $v_2 = 12\sin^{2} \alpha$, where $0 < \alpha < 2\pi$, and $\alpha \neq \pi$.

Consider $(u_n)$ geometric with $a>0$, $0<r<1$, remainder $R_n=S_\infty-S_n$.