12 General U3 T3 Growth and Decay ST1 Arithmetic Sequences

For the sequence 4, 2, 0, –2, –4 ... the common difference is

• 4

• 2

• -2

• -4

BONUS QUESTION: Is there a common difference is this sequence: 1, 3, 9, 27.

• 3

• No

Question 1. A sequence is defined by 𝑎_n= 𝑎_n₋₁ + 14

Given that 𝑎4 = 56, the value of 𝑎₂ is

• 14

• 28

• 42

• 70

Exhibition organisers believe that the number of attendees increases each day as an arithmetic sequence. The organisers know that 353 people attended the first day and 439 people attended the third day.

A) Determine the common difference.

(a)  

Exhibition organisers believe that the number of attendees increases each day as an arithmetic sequence. The organisers know that 353 people attended the first day and 439 people attended the third day. The common difference is 43.

Predict the number of people who will attend the sixth day.

(a)  

A sequence has been defined as 𝑡_n+1 = 𝑡_n + 4, 𝑡₁ = 5

Calculate the 27th term.

(a)  

(P2) A water tank contains 12 500 L of water. The tap is accidentally left on and the tank loses 135 L per minute. The tap is turned off when the tank has 5000 L of water left.

Use a mathematical model to determine how long the tap was left on to the nearest minute. (don't enter units)

(a)  

(P2) In 2011, Chris was earning a salary of $67 500. Chris receives the same pay increase each year and in 2018 was earning a salary of $84 300. In 2015, Sam was earning a salary of $79 500. Sam receives the same pay increase each year and in 2019 was earning a salary of $87 900. Determine when Chris will earn more than Sam.

(a)