IB Mathematics Analysis and Approaches Topic SL…

Find the sum of the first six terms of the geometric progression $64, 48, 36, \dots$

Consider a geometric sequence $(u_n)$ with first term $a>0$ and common ratio $0<r<1$ . Let $S_n$ be the sum of the first $n$ terms, and let $R_n=S_\infty-S_n$ .

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

(b) Suppose $S_5=\dfrac{31}{32}S_\infty$ . Find $r$ .

Consider a geometric sequence with $u_1=\dfrac{18}{5}$ , $r>0$ , and

u_2u_3u_4=\dfrac{729}{64}.

(b) Find the least value of $n$ such that $u_n < 1$ .

A geometric sequence has first term $u_{1}$ and common ratio $r$ , where $r \neq 0$ .

Its third term is $1.5$ .

The sum of its first five terms is $10$ .

(a) Show that $3r^{4}+3r^{3}-17r^{2}+3r+3 = 0$ .

(b) Find all values of $r$ satisfying this equation, and which of them give a series with a sum to infinity.

IB Mathematics Analysis and Approaches SL 1.3—geometric Sequences and Series Questionbank

IB Mathematics Analysis and Approaches SL 1.3—geometric Sequences and Series Questionbank

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IB Mathematics Analysis and Approaches SL 1.3—geometric Sequences and Series Questionbank

IB Mathematics Analysis and Approaches SL 1.3—geometric Sequences and Series Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 1.3—geometric Sequences and Series Questionbank

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