I really need help on this

Arithmetic sequences et sn} be an arithmetic sequence that starts with an initial index of 0. The initial term is 3 and the comm

navik [9.2K]

Answer:

(a) The value of $s_z$ is (z+1)(3-z).

(b) The next term in the sequence is -2.

Step-by-step explanation:

(a)

It is given that arithmetic sequence that starts with an initial index of 0.

The initial term is 3 and the common difference is -2.

$a_0=3$

$d=-2$

We need to find the value of $s_z$ .

$s_z=\sum_{n=0}^{n=z}(a+nd)$

where, a is initial term and d is common difference.

$s_z=\sum_{n=0}^{n=z}(3-2n)$

The sum of an arithmetic sequence with initial index 0 is

$s_n=\frac{n+1}{2}[2a+nd]$

where, a is initial term and d is common difference.

Substitute n=z, a=3 and d=-2 in the above formula.

$s_z=\frac{z+1}{2}[2(3)+z(-2)]$

$s_z=\frac{z+1}{2}[2(3-z)]$

$s_z=(z+1)(3-z)$

Therefore the value of $s_z$ is (z+1)(3-z).

(b)

The given arithmetic sequence is

7, 4, 1, ...

We need to find the term in the sequence.

In the given arithmetic sequence the first term is

$a=7$

The common difference of the sequence is

$d=a_2-a_1\Rightarrow 4-7=-3$

The first term is 7 and common difference is -3.

Add common difference in last given term, i.e., 1, to find the next term of the sequence.

$1+(-3)=1-3=-2$

Therefore the next term in the sequence is -2.

3 0

4 years ago

Solve for W. 4w-4+2(5w+8)=-2(w+3) Simplify your answer as much as possible.

gayaneshka [121]

Answer:

w = $-\frac{9}{8}$

Step-by-step explanation:

The question is $4w-4+2(5w+8)=-2(w+3)$

We can first use distributive property to simplify, the distributive property is $a(b+c)=ab+ac$

Thus we have:

$4w-4+2(5w+8)=-2(w+3)\\4w-4+10w+16=-2w-6$

Now we combine like terms and simplify to get the final answer for w.

$4w-4+10w+16=-2w-6\\14w+12=-2w-6\\14w+2w=-6-12\\16w=-18\\w=\frac{-18}{16}\\w=-\frac{9}{8}$

Thus, w = $-\frac{9}{8}$

8 0

3 years ago

Read 2 more answers

In ΔOPQ, PQ = 17, QO = 9, and OP = 15. Which statement about the angles of ΔOPQ must be true?

77julia77 [94]

Answer:

All angles are different.

Internal angles can be acute, obtuse, or right angle.

The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.

Step-by-step explanation:

Given - In ΔOPQ, PQ = 17, QO = 9, and OP = 15.

To find - Which statement about the angles of ΔOPQ must be true?

Proof -

As given,

In ΔOPQ, PQ = 17, QO = 9, and OP = 15.

As all the sides of the given triangle is different, So the given triangle is a Scalene triangle.

Now,

We know that , In Scalene triangle -

All sides are different.

All angles are different.

Internal angles can be acute, obtuse, or right angle.

The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.

6 0

3 years ago

As of mid-2016, the world's population was about 7.4 billion people. The population of Country A was 226 million. In mid-2016, w

kherson [118]

Answer:

The percentage of country A population to the world population

= 3.05%

Step-by-step explanation:

Country A population as of 2016

= 226 million

= 226000000

The world population as of 2016

= 7.4 billion

= 7400000000

The percentage of country A population to the world population

= Country A population /The world population

The percentage of country A population to the world population

= 226000000/7400000000

The percentage of country A population to the world population

= 0.03054

Now multiplying by 100

= 3.05%

3 0

3 years ago

Help!!!

Jobisdone [24]

Answer:

In the year 2019 the number of new cars purchased will reach 15,000.

Step-by-step explanation:

t = 0 corresponds to the number of new cars purchased in 1998. If that is so, we can determine t ( time ) by making our quadratic equation here equal to 15,000 - considering that we want the year the number of cars reaches this value. t here is only the number of years to reach 15,000 cars, so we would have to add that value to 1998, to see the year that the cars will reach 15,000.

The " set up " should look like the following quadratic equation -

20t² + 135t + 3050 = 15,000 - Isolate 0 on one side,

20t² + 135t - 11950 = 0 - From here on let us solve using the quadratic equation formula,

$t=\frac{-135+\sqrt{135^2-4\cdot \:20\left(-11950\right)}}{2\cdot \:20}:\quad \frac{-27+\sqrt{38969}}{8}$ ,

$t=\frac{-135-\sqrt{135^2-4\cdot \:20\left(-11950\right)}}{2\cdot \:20}:\quad -\frac{27+\sqrt{38969}}{8}$ ... now as you can see we have two solutions, but time can't be negative, and hence our solution is the first one - about 21.3 years. 1998 + 21.3 = ( About ) The year 2019. Therefore, in the year 2019 the number of new cars purchased will reach 15,000.

3 0

3 years ago

Read 2 more answers