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3 years ago

Given a geometric sequence with a1 = 6 and r= 2/3 write an explicit formula for an the nth term of the sequence.

Mathematics

1 answer:

fomenos3 years ago

6 0

the explicit formula for aₙ the nth term of the sequence will be: $a_{n}=6\times (\frac{2}{3})^{n-1}\\$

Step-by-step explanation:

The explicit formula of geometric sequence is of the form:

$a_{n}=a_{1}r^{n-1}$

where a₁ is the first term and r is the common ratio.

We are given:

a₁ = 6

r = 2/3

Putting values in the formula:

$a_{n}=a_{1}r^{r-1}\\a_{n}=6\times (\frac{2}{3})^{n-1}\\$

So, the explicit formula for aₙ the nth term of the sequence will be: $a_{n}=6\times (\frac{2}{3})^{n-1}\\$

Keywords: Explicit formula for geometric sequence

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Suppose that the area between a pair of concentric circles is 49pi. Find the length of a chord in the larger circle that is tang

Lapatulllka [165]

Answer:

14 units

Step-by-step explanation:

We are given that the area between two concentric circles is $49\pi$

We have to find the length of chord in the larger circle that is tangent to the smaller circle.

Let $r_1,r_2$ be the radius of two circles.

$r_1$ be the radius of small circle and $r_2$ be the radius of large circle

We know that area pf circle= $\pi r^2$

Area of large circle = $\pi r^2_2$

Area of small circle = $\pi r^2_1$

Area between two circles = $49\pi$

Area of large circle -Area of small circle= $49\pi$

$\pi r^2_2-\pi r^2_1=49\pi$

$\pi(r^2_2-r^2_1)=49$

By pythagorus theorem

$AD^2=OA^2-OD^2$

$AD^2=r^2_2-r^2_1$

$AD=49$

$AD=\sqrt{49}=7$

Length of chord= $2\cdot AD$

Hence, the length of chord of the larger circle = $2\cdot7=14$ units

7 0

3 years ago

Read 2 more answers

Brian invests £990 into his bank account. He receives 2% per year simple interest. How much

nata0808 [166]

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \£990\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &4 \end{cases} \\\\\\ A=990[1+(0.02)(4)]\implies A=990(1.02)(4)\implies A=4039.2$