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3 years ago

Find the 7th term of the geometric sequence -2, 6, -18, 54, -162, ...

Mathematics

1 answer:

AlladinOne [14]3 years ago

4 0

Answer:

-1458

Step-by-step explanation:

Let's find the rule of the sequence. It seems that each term is -3 times the previous term.

Let's continue the sequence.

486, -1458

-1458 is the 7th term

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Tavon has a gift card for $85 that loses $3.50 for each 30-day period it is not used. He has another gift card for $75 that lose

miskamm [114]

Answer:

Each card will have a value of $15 when they equal after 600 days which also is 20 30-day periods.

Step-by-step explanation:

Card1: $85 - \frac{3.50}{30} x$

Card2: $75 - \frac{3}{30} x$

x is number of days

$85 - \frac{3.50}{30} x = 75 - \frac{3}{30} x$

2550 - 3.50x = 2250 - 3x

2550 - 0.50x = 2250

-0.50x = -300

x = 600 days

Card1: $85 - \frac{3.50}{30} (600)$

85 - 70 = 15 dollars

Card2: $75 - \frac{3}{30} (600)$

75 - 60 = 15 dollars

3 0

3 years ago

Pleaseeee help meeeee

Alla [95]

The checked answers you have are correct.

3 0

3 years ago

Does the following infinite series converge or diverge? 1/3+2/9+4/27+8/81+...

PilotLPTM [1.2K]

Note that A and D are ludicrous choices, so you can throw them away outright. (Any divergent series cannot have a sum, and any convergent series must have a sum.)

The sum is certainly convergent because it can be written as a geometric sum with common ratio between terms that is less than 1 in absolute value.

$S=\dfrac13+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots$
$S=\dfrac13\left(1+\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\cdots\right)$

We can then find the exact value of the sum:

$\dfrac23S=\dfrac13\left(\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\dfrac{2^4}{3^4}+\cdots\right)$

$\impliesS-\dfrac23S=\dfrac13$
$\implies\dfrac13S=\dfrac13$
$\implies S=1$

So the answer is B.

8 0

3 years ago

If j = k, then j + 9 = k + 9 represents which algebraic property

sleet_krkn [62]

Answer:

c) The given expression represents Addition Property of Equality.

Step-by-step explanation:

Here, the given expression is j = k

Now by ADDITION PROPERTY OF EQUALITY:

The property that states that if you add the same number to both sides of an equation, the sides remain equal.

So, if A = B ⇒ A + x = B + x

Now, here given that j = k

If we add the same number 9 on both the sides, the equation remains undisturbed.

⇒ j + 9 = k + 9

Hence, the above expression represents Addition Property of Equality.

8 0

4 years ago

What is the perimeter

Mademuasel [1]

Good morning ☕️

Answer:

Perimeter = 36 cm

Step-by-step explanation:

Firstly, Check the attached picture

perimeter = 10 + 10 + 8 + 8

= 20 + 16

= 36

5 0

3 years ago