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Degger [83]
3 years ago
13

Write an explicit formula for An, the nth term of the sequence 7, -42, 252, ....

Mathematics
1 answer:
erik [133]3 years ago
8 0

Answer:

A_n = 7(-6)^{n-1}

Step-by-step explanation:

<u>Key skills needed: Explicit formula, Geometric sequence</u>

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7   or   252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

a_n = a_1(r)^{n-1}

--> r means the constant (or common ratio) that is being multiplied.

--> a_1 means the first term

--> a_n means the "nth" numbered term (so a_3 is the 3rd term, a_{10} is the 10th term and so on).

--> n-1 is just the "n" in a_n minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> r = -6 (Since we got -6 as the constant/common ratio).

--> a_1  = 7 (Since 7 is the 1st term)

This means that our formula would be --> A_n = 7(-6)^{n-1}

<em>Hope you understood and have a nice day!! :D</em>

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Answer:

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Step-by-step explanation:

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The number of people that claimed more than one game as their favorite (X) is given by:

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Those people can be divided in B&F only, B&M only, M&F only and B&M&F:

X=(B\&M-B\&M\&F)+(B\&F-B\&M\&F)+(M\&F-B\&M\&F)+B\&M\&F\\X=B\&M+B\&F+M\&F-2*B\&M\&F\\22=10+15+M\&F-2*5\\M\&F=7\ people

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Step-by-step explanation:

Given that Linda has played 16 turns and has obtained 34 points, taking into account that in each turn she can obtain 2 or 3 points, to determine the number of turns in which she obtained 2 points, the following table must be performed:

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