SL 1.2—Sequences and Sigma Notation Questionbank

It is known that the number of fish in a certain pond will decrease by $7\%$ each year unless some new fish are added. At the end of each year, 250 new fish are added to the pond.

At the start of 2018, there are 2500 fish in the pond.

A software company is tracking the number of downloads of its app, where the downloads at month $n$ are defined by the sequence $u_n = 10^n$.

Rosa joins a club to prepare to run a marathon. During the first training session Rosa runs a distance of 3000 metres. Each training session she increases the distance she runs by 400 metres.

A marathon is 42.195 kilometres.

In the $k$th training session Rosa will run further than a marathon for the first time.

Carlos joins the club to lose weight. He runs 7500 metres during the first month. The distance he runs increases by 20% each month.

A student is building a robot that is coded to take a certain number of steps. The first day it takes 1 step, the second day it takes 2 steps, the third day it takes 3 steps, and so on. Hence on the $n$th day it takes $n$ steps.

A pyramid of stacked cubes is being built for a mathematics exhibition to promote STEM education. The first level has 10 cubes, the second level has 12 cubes, and each additional level contains 2 more cubes than the previous level. The organisers have 1500 cubes available.

In scientific research, measurements are often rounded to a certain number of significant figures. Understanding the range of possible values based on these figures is important for data analysis.

A research study is analyzing the growth of a plant species, where the growth at month $n$ is defined by the sequence $u_n = 10n^2$.

In mathematics, numbers can belong to different sets: natural numbers ($\mathbb{N}$), integers ($\mathbb{Z}$), rational numbers ($\mathbb{Q}$), and real numbers ($\mathbb{R}$). A Venn diagram shows these sets, with each set nested within $\mathbb{R}$ as follows: $\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}$.

Given the numbers $14$, $-3$, $\pi$, $-0.3$, $2.7 \times 10^3$, and $3.4 \times 10^{-2}$, place each in the appropriate region of the Venn diagram for $\mathbb{N}, \mathbb{Z}, \mathbb{Q},$ and $\mathbb{R}$.

A startup is analyzing its revenue growth, defined by the recursive formula ${u_1 = 10}$, ${u_{n+1} = 2u_n + 10}$.

In a physics experiment, two values are measured: one representing a large distance and the other a very small distance. These values are essential for calculations in the study of forces and interactions. Let $x = 2.6 \times 10^4$ and $y = 5.0 \times 10^{-8}$.