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1)) Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence where n=1 for the first term. -10,(-20)/(3),(-40)/(9),ldots 1)) Write your answer using proper fractions,improper fractions, and integers. a_(n)=square (square )^n-1

Question

1)) Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence where n=1 for the first term. -10,(-20)/(3),(-40)/(9),ldots 1)) Write your answer using proper fractions,improper fractions, and integers. a_(n)=square (square )^n-1

1)) Write an equation to describe the sequence below. Use n to represent the position of a
term in the sequence where n=1 for the first term.
-10,(-20)/(3),(-40)/(9),ldots 
1)) Write your answer using proper fractions,improper fractions, and integers.
a_(n)=square (square )^n-1

Solution

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DanteMaster · Tutor for 5 years

Answer

### $a_n = -10(\frac{2}{3})^{n-1}$

Explain

## Step 1: Identify the first term<br />### The first term, $a_1$, is -10.<br /><br />## Step 2: Calculate the common ratio<br />### Divide the second term by the first term: $\frac{-20/3}{-10} = \frac{2}{3}$. Divide the third term by the second term: $\frac{-40/9}{-20/3} = \frac{2}{3}$. The common ratio, $r$, is $\frac{2}{3}$.<br /><br />## Step 3: Construct the equation<br />### Plug $a_1 = -10$ and $r = \frac{2}{3}$ into the formula $a_n = a_1(r)^{n-1}$ to get $a_n = -10(\frac{2}{3})^{n-1}$.
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