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Solve (9th grade math)

Solve (9th grade math)-example-1

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Answer:

1. Geometric Sequence Equation for Table A:


\boxed{\tt a_n = a_1 * r^((n-1))}

2. Arithmetic Sequence Equation for Table B:


\boxed{\tt a_n = a_1 + (n-1) * d}

3.

  • 20th term for Geometric Sequence:

    \boxed{\tt a_(20) = a_1 * r^(19)}
  • 20th term for Geometric Sequence:

    \boxed{\tt a_(20) = a_1 + 19* d}

Explanation:

1. Geometric Sequence Equation for Table A:

The geometric sequence equation is given by the formula:


\tt \[a_n = a_1 * r^((n-1))\]

where:


  • \tt \(a_n\) represents the nth term of the sequence.

  • \tt \(a_1\) is the first term of the sequence.

  • \tt \(r\) is the common ratio.

For Table A, since we don't have the actual values, we can represent the equation as:


\boxed{\tt a_n = a_1 * r^((n-1))}


\hrulefill

2. Arithmetic Sequence Equation for Table B:

The arithmetic sequence equation is given by the formula:


\tt a_n = a_1 + (n-1) * d

where:


  • \tt \(a_n\) represents the nth term of the sequence.

  • \tt \(a_1\) is the first term of the sequence.

  • \tt \(d\) is the common difference.

For Table B, since we don't have the actual values, we can represent the equation as:


\boxed{\tt a_n = a_1 + (n-1) * d}


\hrulefill

3. Finding Term 20 for both sequences:

In order to find the 20th term for both sequences, we need the actual values for
\tt \(a_1\), \(r\) and d.

in the case of Table A


\tt a_(20) = a_1 * r^((20-1))


\boxed{\tt a_(20) = a_1 * r^(19)}

in the case of Table B.


\tt a_(20) = a_1 + (20-1) * d


\boxed{\tt a_(20) = a_1 + 19* d}

By using this formula, we can easily fill up the box.

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