IB Mathematics Applications & Interpretation Topic SL…

For a geometric progression, the third term is $6$ and the sixth term is $\frac{2}{9}$ .

(a) the common ratio for this progression.

(b) the sum to infinity for this specific progression.

A clip's daily reposts form a geometric sequence. Day 5 has $48$ reposts and day 8 has $384$ .

(a) the common ratio.

(b) the number of reposts on day 1.

A podcast's weekly downloads form a geometric sequence. Week 4 has $54$ downloads and week 7 has $1458$ .

(b) the number of downloads in week 1.

Consider the infinite geometric sequence $a_n$ , where $a_n = 4(-2)^{n-1}$ .

Consider the infinite geometric sequence $b_n$ , where $b_n = 4(2)^{n-1}$ .

A third sequence $c_n$ is defined as $c_n = a_n + b_n$ .

The finite series $\sum_{k=1}^{150} c_k$ can be expressed in the form $\sum_{k=0}^{N} 8q^k$ .

(b) Find the common ratio $q$ .

(a) the common ratio.

(c) Let $S_k$ be the total number of reposts in the first $k$ days. the minimum integer value of $k$ such that $S_k>6000$ .

For a geometric sequence, the second term is $u_2=-48$ and the fifth term is $u_5=6$ . the value of the first term in this sequence.

(c) Let $S_k$ be the total number of downloads in the first $k$ weeks. the minimum integer value of $k$ such that $S_k>5000$ .

(a) the first three non-zero terms of the sequence $c_n$ .

IB Mathematics Applications & Interpretation SL 1.3—geometric Sequences Questionbank