IB Mathematics Analysis and Approaches Topic SL…

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

Find the two possible values of the first term.

Show that, for the two possible geometric progressions, $u_{n2}=3^{n-2}u_{n1}$ .

The sum of the first two terms of a geometric progression is $50$ , and the sum to infinity is $\frac{160}{3}$ .

The second term of a geometric progression is $12$ and its fourth term is $\frac{27}{4}$ .

Consider the infinite series

S = \log_a(1) + \log_a(r) + \log_a(r^2) + \log_a(r^3) + \dots ,

Consider a geometric sequence $(u_n)$ with first term $a>0$ and common ratio . Let be the sum of the first terms, and let .

Find the possible values of the common ratio $r$ .

Hence find the corresponding possible values of the first term $a$ .

Given that the common ratio is positive, find the sum to infinity of the progression.

Show that the $n$ -th partial sum can be written as

S_n = \log_a(r^{0+1+2+\dots+(n-1)}).

Deduce that

S_n=\frac{n(n-1)}{2}\,\log_a(r).

Prove that $R_n=\dfrac{ar^n}{1-r}$ .

Suppose $S_5=\dfrac{31}{32}S_\infty$ . Find .

IB Mathematics Analysis and Approaches SL 1.8—sum of Infinite Geo Sequence Questionbank