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3 years ago

The third term of an arithmetic sequence is $5$ and the eighth term is $-20$. What is the product of the 4th and 2015th terms?

Mathematics

1 answer:

Andreas93 [3]3 years ago

5 0

Answer:

Step-by-step explanation:

Let n be the first term of this sequence and d the difference between two consecutive terms.

Following the arithmetic sequence formula,

The equation for the 3rd term:

n + 2d = 5

and the equation for the 8th term:

n + 7d = -20

We should start by finding d by subtracting the second equation from the first.

n + 2d - (n + 7d) = 5 - (-20)

-5d = 25

d = -5

We can then find the 1st term by plugging this number into the first equation.

n + 2 * -5 = 5

n - 10 = 5

n = 15

Now, using once again the arithmetic sequence formula, find the equation for the fourth term.

n + (4 - 1)*d

Plug in the values we found previously and solve:

15 + (4 - 1)*-5

= 15 + 3*-5

= 15 + (-15)

= 0

The 4th term is 0.

Remember that this problem is asking for the product of the 4th term and the 2015th term, and anything times zero equals to zero, so we don't even need to solve for the 2015th term!

Therefore, the answer to this problem is 0.

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HELP PLZ questions in pictures above

lisov135 [29]

Answer:

S1) False. 2³ is 2 × 2 × 2 which is 8, not 6.

S2) False. ( 2x / 3y ^ (2) ) ^ (3) =

( (2x) ^ (3) / ( (3y) ^ (2) ) ^ (3) ) = (2)³ × (x)³ / (3)³ × (y²)³ = 8 × x³ / 27 × y⁶ = 8x³ / 27y⁶.

i.e (a^b)^c = a^(b × c).

S3) True.

S4) True.

S5) False. x^(-3) = 1 / x^(3) ≠ 1 / 3x

6 0

3 years ago

Candy counted to 600 by 6's, beginning with 6. Danny counted to 600 by 4's beginning with 4. How many the numbers that candy cou

KATRIN_1 [288]

Step-by-step explanation:

If we count for both numbers up to 36, we start seeing a pattern...

Candy: 6 12 18 24 30 36

Danny: 4 8 12 16 20 24 28 32 36

Every other number in Candy's counting is also counted by Danny. So here's what we'll do:

Divide 600 by 6

600/6 = 100

This is how many numbers Candy counted overall.

Divide the result by 2.

100/2 = 50

This is how many numbers Danny counted that were also numbers Candy counted.

Answer:

50 of the numbers that candy counted were also counted by Danny.

8 0

3 years ago

Read 2 more answers

PLEASE: Find The Ending Balence

eimsori [14]

Using exponential functions, the ending balances are given as follows:

1. $1,490.07.

2. $1,073.83.

3. $358.04.

<h3>What is an exponential function?</h3>

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^t$

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

Item a:

The parameters are:

A(0) = 939, r = 0.08, t = 6.

Hence the balance is:

$A(6) = 939(1.08)^6 = 1490.07$

Item b:

The parameters are:

A(0) = 823, r = 0.03, t = 9.

Hence the balance is:

$A(9) = 823(1.03)^9 = 1073.83$

Item c:

The parameters are:

A(0) = 269, r = 0.1, t = 3.

Hence the balance is:

$A(9) = 269(1.1)^3 = 358.04$

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

4 0

2 years ago

Read 2 more answers

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Brilliant_brown [7]

Answer:

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Step-by-step explanation:

6 0

3 years ago

you toss a ball that travels on the path y= -0.1x^2 + 2x+4 where x and y are measured in meters. Sketch the path of the ball. Ho

Y_Kistochka [10]

Answer:

The ball goes 14 meters high

Step-by-step explanation:

Given the function

y= -0.1x^2 + 2x + 4

In the figure attached, the function is shown.

The maximum height is equivalent to the vertex of the function, which is obtained as follows:

Xv = -b/(2a) = -2/(2*-0.1) = 10

Yv = -0.1Xv^2 + 2Xv + 4

Yv = -0.1(10)^2 + 2(10) + 4 = 14

8 0

4 years ago