Find the 17th term of the sequence: -11, -9, -7, -5,

The trees at a national park have been increasing in numbers. There were 1,000 trees in the first year that the park started tra

ivanzaharov [21]

The sequence forms a Geometric sequence as the rule to obtain the value for the next term is by ratio

Term 1: 1000
Term 2: 200
Term 3: 40

From term 1 to term 2, there's a decrease by $\frac{1}{5}$
From term 2 to term 3, there's a decrease also by $\frac{1}{5}$

The rule to find the $n^{th}$ term in a sequence is
$n^{th}=a r^{n-1}$ , where $a$ is the first term in the sequence and $r$ is the ratio

So, the formula for the sequence in question is
$n_{th}$ term = $1000( \frac{1}{5} ^{n-1} )$

The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.

We can find a partial sum of the sequence using the formula
$S_{∞} = \frac{a}{1-r}$ for -1<r<1
Substituting $a=1000$ and $r= \frac{1}{5}$ we have
$S_{∞}$ = $\frac{1000}{1- \frac{1}{5} }$ = 1250

Hence, the correct option is option number 1

6 0

3 years ago

How do I determine which is y=-1/3x+2?

Jlenok [28]

Step-by-step explanation:

This is a linear equation in slope intercept form which is

$y = mx + b$

where m is the slope and b is the y intercept.

The equation

$y = - \frac{1}{3} x + 2$

Has a slope of -1/3 so this means that the slope will be decreasing. A negative linear equation increases as we go left. and decreases as we go right. The y intercept is 2. So this means the graph must pass through (0,2) and when x=0, y must be 2.

In other words, look for a line that the y values increase as we go left and decrease we go right. Also look for a point (0,2) and make sure the graph pass through it.

6 0

3 years ago

5(2+(-9))+-25<br> HELP<br> PLZZ

Gelneren [198K]

Answer: -60

Step by step
5 (2 - 9) -25
Start by distributing which will give you
10 - 45 - 25
Combine your like terms giving you
-60

7 0

2 years ago

Read 2 more answers

What is the Point slope equation

anastassius [24]

Answer:

y - y1 = m(x - x1)