How to convert oz to liters

Find the 8th term of the geometric sequence whose common ratio is 2/3 and whose first term is 7

motikmotik

Answer:

The 8th term of the sequence is 896/2187.

Step-by-step explanation:

We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.

We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:

$\displaystyle x_{n} = a\left(r\right)^{n-1}$

Where a is the initial term and r is the common ratio.

Substitute:

$\displaystyle x_{n} = 7\left(\frac{2}{3}\right)^{n-1}$

To find the 8th term, let n = 8. Substitute and evaluate:

$\displaystyle \begin{aligned} x_{8} &= 7\left(\frac{2}{3}\right)^{(8) - 1} \\ \\ &= 7\left(\frac{2}{3}\right)^{7} \\ \\ &= 7\left(\frac{128}{2187}\right) \\ \\ &= \frac{896}{2187} = 0.4096...\end{aligned}$

In conclusion, the 8th term of the sequence is 896/2187.

8 0

3 years ago

If the world's population increased exponentially from billion in 1998 to billion in 2008 and continued to increase at the same

Gelneren [198K]

Answer:

The answer is "7.122 billion"

Step-by-step explanation:

Please find the complete question in the attached file.

Using formula:

$\to y=Ce^{kt}$

$C=5.937\\\\y=6.771\\\\t=10\\\\ k=?6.771=5.937e^{10k}\\\\1.1405=e^{10k}\\\\\ln(1.1405)={10\ k}\\\\0.013={k}\\\\$

So,

$\to y=5.937e^{.013t}\\\\$

when it becomes $2012, \ t=14$ so plug the value into the formula

$\to y= 5.937e^{.013(14)} =7.122 \ billion$

7 0

3 years ago

What is the height of an equilateral triangle with side lengths of 14?

olganol [36]

If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.
If Each side of an equilateral triangle is 10 m. ... Thus triangle APC is a righttriangle. The length of CA is 10 m, and the length of PC is 5 m, and hence you can use Pythagoras' theorem to find the length of AP, which is the height of the triangleABC.

5 0

3 years ago

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Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

andreev551 [17]

Answer:

816 square feet

Step-by-step explanation:

13(16+20+12) + 16(12) = 816

7 0

3 years ago

Solve the equation for x. 15 = -2x + 3

bekas [8.4K]

Answer:

Step-by-step explanation:

$-2x+3=15\qquad\text{subtract 3 from both sides}\\\\-2x+3-3=15-3\\\\-2x=12\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{2}=\dfrac{12}{-2}\\\\x=-6$

6 0

3 years ago

Read 2 more answers