All categories

2 years ago

The sum of the first 15 terms of the sequence an=10n+21

1 answer:

3 0

That is
the sum of all the terms from a1 to an when you are summing up n terms is n(a1+an)/2
so

find the 1st and 15th term
1st term is a1=10(1)=21=10+21=31
15th term is a15=10(15)+21=150+21=171

and n=15
15(31+171)/2=15(202)/2=3030/2=1515
the sum of the first 15 term is 1515

You might be interested in

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

Nataly_w [17]

Answer: 0.1289

Step-by-step explanation:

Given : The proportion of all students at a large university are absent on Mondays. : $p=0.15$

Sample size : $n=12$

Mean : $\mu=np=12\times0.15=1.8$

Standard deviation = $\sigma=\sqrt{np(1-p)}$

$\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369$

Let x be a binomial variable.

Using the standard normal distribution table ,

$P(x=4)=P(x\leq4)-P(x\leq3)$ (1)

Z score fro normal distribution:-

$z=\dfrac{x-\mu}{\sigma}$

For x=4

$z=\dfrac{4-1.8}{1.2369}\approx1.78$

For x=3

$z=\dfrac{3-1.8}{1.2369}\approx0.97$

Then , from (1)

$P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289$

Hence, the probability that four students are absent = $0.1289$

3 0

2 years ago

Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as

ikadub [295]

Answer:

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

gil owns a life insurance policy that he purchased when he first graduated college it has a 100000 death benefit and gil pays pr

Scorpion4ik [409]

The insurance Gil has is most likely individual life insurance.

7 0

2 years ago

Read 2 more answers

This unit focused, in part, on relationships in triangles. A triangle is the simplest type of polygon and is frequently used in

Galina-37 [17]

The answers are as follows:
1. Triangles are often used to build different types of support structures because of its beneficial properties. Triangles is rigid in shape and it has strength. When force is applied to the side of a triangle, it can not shift into another shape, this is because its sides and angles are fixed.
2. The properties of triangle that make it a desirable geometric shape for building support structures is its fixed sides, fixed angles, rigidity and strength. Triangles are the strongest shapes and they are stable. Thus, triangle can be easily fix together to provide strength and stability over a wide area.
3. There are different types of triangles, these include: equilateral triangle, scalene, isosceles, right triangle, obtuse and acute. Of all these triangles, the best triangle is equilateral triangle.
4. Triangle is preferred over other types of polygon because, it is the strongest. The other polygons can be bent into different other forms that are not regular polygon, but a triangle always retains its shape and can not be deformed.

6 0

2 years ago

Read 2 more answers

In 154 N38 what digit should be replaced to N to make the number divisible by 3,6 and 9?

JulsSmile [24]

Answer:

$N = 6$ so that number becomes divisible by 3, 6 and 9.

Step-by-step explanation:

In Number Theory there is a rule of thumb which states that sum of digits of a multiple of 3 equal 3 or a multiple of three. If we know that $n = 154N38$ , then its sum of digits is: