3.10 Arithmetic Sequences

Determine if the following sequences are arithmetic sequences. Explain your reasoning.

1. $\left\{4 , 7 , 10 , 13 , 16 , 19 , 22 , 25 , ...\right\}$
2. $\left\{20 , 40 , 80 , 160 , 320 , 640\right\}$
3. $\left\{7 , 1 , - 5 , - 11 , - 17 , - 23 , - 29 , - 34 , - 40\right\}$

Identify $a_{1}$ and $d$ for the following arithmetic sequence. Use this information to determine the $60 \text{th}$ term.

A sequence is known to be arithmetic. Two of its terms are $a_{7} = 56$ and $a_{19} = 104$. Use that information to find the constant difference, the first term, and then the $50 \text{th}$ term of the sequence.

What is the sum of the first 60 terms of an arithmetic sequence with $a_{1} = 4.5$ and $d = 2.5$?

Jordan has just watched The Queen’s Gambit and decided to hone their skills in chess. To really improve at the game, Jordan decides to practice for 3 hours the first week, and increase their time spent practicing by 30 minutes each week. How many hours will Jordan practice chess in week 20?

Let’s check back in on Jordan. Recall, Jordan had just watched The Queen’s Gambit and decided to hone their skills, practicing for 3 hours the first week, and increasing the time spent practicing by 30 minutes each week. How many hours total will Jordan have practiced chess after 30 weeks of practice?