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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 :

The answer is 286.

Explanation:
We first find the first term of the sequence, a₁. We use the explicit formula for an arithmetic sequence to do this: 

[tex]a_n=a_1+d(n-1)[/tex]

We know the 6th term is 22; this means we substitute 6 in for n. We also know the common difference is 6, so we use that for d. That gives us a₆=a₁+6(6-1).

We know the value of the sixth term is 22, so we use that instead of a₆:

22=a₁+6(6-1).

Evaluating this, we have
22=a₁+6(5)
22=a₁+30.

Subtract 30 from both sides, and we have
22-30=a₁
-8=a₁.

We now use this value in our explicit formula: 

[tex]a_n=-8+6(n-1)[/tex]

To find the fiftieth term we replace n with 50:
a₅₀= -8+6(50-1)
a₅₀= -8+6(49)
a₅₀= -8+294
a₅₀=286

Answer:

286

Step-by-step explanation:

When solving this problem you need to use an explicit formula for an arithmetic sequence to properly answer this question. I hope this helped!❤

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