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garik1379 [7]
3 years ago
13

Let me know the answer plz

Mathematics
1 answer:
Gala2k [10]3 years ago
7 0

<u>Answer:</u>

The correct answer option is H. 4374.

<u>Step-by-step explanation:</u>

We are given the following geometric sequence and we are to find its 8th term:

\frac{2}{9}, \frac{2}{3}, 2,...

Here a_1=\frac{2}{9} and common ratio (r) = \frac{\frac{2}{3} }{\frac{2}{9} } =3.

The formula we will use to find the 10th term is:

nth term = a_1 \times r^{(n-1)}

Substituting the values in the formula to get:

10th term = \frac{2}{9} \times 3^{(10-1)}

10th term = 4374

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Solution

1) Simplify \frac{4}{7y}<span> to </span>\frac{4y}{7}
\frac{4y}{7} <span>−2= </span>\frac{3}{7} + \frac{3}{14}

2) Simplify \frac{3}{7} + \frac{3}{14} <span>to <span>914</span>
</span>\frac{4y}{7} <span>−2= </span>\frac{9}{14}

3) <span>Add 2 to both sides
</span>\frac{4y}{7} = \frac{9}{14} <span>+2
</span>
4) Simplify \frac{9}{14&#10;} <span><span>+2</span> to </span>\frac{37}{14}
\frac{4y}{7} = \frac{37}{14}

5) <span>Multiply both sides by 7
</span><span>4y= </span>\frac{37}{14} <span>×7
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6) Simplify \frac{37}{14} <span><span>×7</span> to </span>\frac{259}{14}
\frac{4y}{7} =\frac{259}{14}

7) Simplify \frac{259}{14}<span> to </span>\frac{37}{2}
\frac{4y}{7} = \frac{37}{2}

8) <span>Divide both sides by 4
</span>y= \frac{37}{2} <span>×4
</span>
9) <span>Simplify <span>2×4</span> to 8
</span><span>y=</span>\frac{37}{8}
<span><span>
Hope this helps 

</span></span>
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3 years ago
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