3 years ago

What is the 8th term of the following geometric sequence? 3, 15, 75, 375, …

1 answer:

3 0

$a_1=3\\a_2=3\cdot5=15\\a_3=15\cdot5=75\\a_4=75\cdot5=375\\\vdots\\\\\text{The general term of a geometric sequence}\ a_n=a_1r^{n-1}\\\\a_1-first\ term\\r-common\ ratio\\\\a_1=3,\ r=5\\\\\text{substitute}\\\\a_n=3(5^{n-1})\\\\8th\ term\to a_8\\\\\text{Substitute}\ n=8\ \text{to the equation of}\ a_n:\\\\a_8=3(5^{8-1})=3(5^7)=3(78125)=234,375\\\\Answer:\ 8th\ term=234,375$

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$y = \frac{1}{3}x-4$

Step-by-step explanation:

Step 1: Solve for y in the first equation

$3y - x = -12$

$3y - x + x = -12 + x$

$\frac{3y}{3} = \frac{x}{3} - \frac{12}{3}$

$y = \frac{1}{3}x - 4$

Step 2: Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1/3 which means that our slope is also going to be 1/3. We also know that our line crosses the point (18, 2) which means that we can use the point slope form to determine our equation

Point Slope Form → $(y-y_1) = m(x - x_1)$