Question

You are playing an Algebra 1 board game with your friends in Mr. Harris's class. It is your turn. You roll the dice and move your token to the next box in the board. You are in the Arithmetic Sequence section of the game. You pick a clue card and one of your partners asks you a question. In order to stay alive in the game, you need to answer correctly. You pick the card below.
The sixth term is 22 and the common difference is is 6.

The question your partner poses to you is “What is the fiftieth term?”

Answer 1

Answer: 286

Step-by-step explanation:

The formula to calculate the nth term of arithmetic sequence is given by :-

$a_n=a+(n-1)d$, where a is the first term and d is the common difference.

Given: The sixth term $a_6= 22$ and the common difference d= 6.

Substitute n=6 in the above formula, we get

$a_6=a+(6-1)6=22\\\\\Rightarrow\ a+30=22\\\\\Rightarrow\ a=22-30=-8$

Now, the fiftieth term is given by substituting n=50 in the above formula, we get

$a_{50}=-8+6(50-1)=-8+6(49)=-8+294=286$

Hence, the  fiftieth term = 286

Answer 2

From here, we need to start by making an equation:

We know that it has a common difference of 6, thus, the slope is -6.

22 = -6(6) + b
b = 58

So we have our equation:

$y = -6x + 58$

Let's plug 50 in and we get -242