The first three terms of a geometric sequence are shown below.

1 answer:

8 0

$a_1=x+3\\\\a_2=-2x^2-6x=-2x(x+3)\\\\a_3=4x^3+12x^2=-2x(-2x^2-6x)=-2x[-2x(x+3)]\\\vdots\\\text{The general term of geometric sequence}\ a_n=a_1r^{n-1}\\\\a_1-first\ term\\r-common\ ratio\\\\a_1=x+3,\ r=-2x\\\\\text{Substitute}\\\\a_n=(x+3)(-2x)^{n-1}\\\\8th\ term\to a_8\\\\\text{Substitute}\ n=8\ \text{to the equation of}\ a_n:\\\\a_8=(x+3)(-2x)^{8-1}=(x+3)(-2x)^7=(x+3)(-128x^7)\\\\\text{use distributive property}\\\\a_8=(x)(-128x^7)+(3)(-128x^7)\\\\\boxed{a_8=-128x^8-384x^7}$

You might be interested in

james and bethany morrison are celebrating their 10th anniversary by having a reception at a local reception hall. they have bud

saveliy_v [14]

Answer:

They can invite 136 while staying in budget

Step-by-step explanation:

Firstly, you know they will have to pay an $80 cleaning fee, therefore, you can subtract 80 from 5,000:

5,000-80 = 4,920

After doing this, you can take 4,920 and divide it by 36 (the price per person).

4,920/36 = 136.67

Because you can not have .67 of a person, your closest number you can use is 136.

leaving them with $24

5 0

3 years ago

Read the following description of a

Annette [7]

Answer:

$\sf a = \boxed{\bf 1} \ n+ \boxed{\bf 3}$

Explanation:

$\sf \underline{rate} \ = \ \sf \dfrac{y_2-y_1}{x_2-x_1} \ = \ \dfrac{rise}{run} \ = \ \dfrac{11-10}{8-7} \ = \ \underline{1}$

<u>Equation</u>:

$\Rightarrow \sf a - a1 = m(n - n1)$

$\Rightarrow \sf a - 10 = 1(n -7)$

$\Rightarrow \sf a = n - 7 + 10$

$\Rightarrow \sf a = n + 3$

3 0

2 years ago

If you can explain your answer that’d be great!! Thank you!

Rasek [7]

Answer:

$A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}$

Step-by-step explanation:

This half life exponential decay equation goes by the formula:

$A(t)=A_{0}e^{kt}$

Where

$k=\frac{ln(\frac{1}{2})}{Half-Life}$

Since half life is given as 22, we plug that into "Half-Life" in the formula for k and then plug in the formula for k into the exponential decay formula:

So,

$k=\frac{ln(\frac{1}{2})}{Half-Life}\\k=\frac{ln(\frac{1}{2})}{22}$