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Taya2010 [7]
3 years ago
8

In a geometric sequence, the common ratio is -5. The sum of the first 3 terms is 147. What is the value of the first term of the

sequence?
Mathematics
1 answer:
Gelneren [198K]3 years ago
5 0

\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill

\bf \begin{cases} r=-5\\ n=3\\ S_3=147 \end{cases} \implies 147=a_1\left( \cfrac{1-(-5)^3}{1-(-5)} \right)\implies 147=a_1\left( \cfrac{1-(-125)}{1+5} \right) \\\\\\ 147=a_1\cdot \cfrac{126}{6}\implies 147=21a_1\implies \cfrac{147}{21}=a_1\implies 7=a_1

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Graph the solution of this inequality: 3/4(x+8) > 1/2 (2x + 10)
miss Akunina [59]
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Interval Notation-

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7 0
3 years ago
Find the values of x and y : EK= 7x+5, KG= 3x+17, HK= 3y-11, KF= y+5<br>NEED ANSWER ASAP
Mice21 [21]

Answer:

<h2>x = 3, y = 8</h2>

Step-by-step explanation:

We know:

The diagonals of the parallelogram are divided in half.

Therefore

EK ≅ KG and HK ≅ KF.

We have

EK = 7x + 5, KG = 3x + 17, HK = 3y - 11 and KF = y + 5

Equations:

(1)   7x + 5 = 3x + 17

(2) 3y - 11 = y + 5

Solutions:

(1)

7x + 5 = 3x + 17       <em>subtract 5 from both sides</em>

7x + 5 - 5 = 3x + 17 - 5

7x = 3x + 12       <em>subtract 3x from both sides</em>

7x - 3x = 3x - 3x + 12

4x = 12           <em>divide both sides by 4</em>

4x/4 = 12/4

x = 3

------------------------------

(2)

3y - 11 = y + 5                <em>add 11 to both sides</em>

3y - 11 + 11 = y + 5 + 11

3y = y + 16         <em>subtract y from both sides</em>

3y - y = y - y + 16

2y = 16           <em>divide both sides by 2</em>

2y/2 = 16/2

y = 8

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3 years ago
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mr Goodwill [35]
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Solve 1/3x - 2/7x &gt; 1/3
Ne4ueva [31]

Answer: x > 7

    Step-by-step explanation:

Given:

\displaystyle \frac{1}{3}x- \frac{2}{7}x > \frac{1}{3}

Subtract:

\displaystyle \frac{1}{21}x > \frac{1}{3}

Divide both sides of the equation by \frac{1}{21}:

\displaystyle x > 7

    <u>What does this mean?</u>

This means the x is equal to all values greater than 7.

-> 7.432421, 7.5, 8, 250, etc

6 0
2 years ago
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