7g2 + 3g − 2, 8g2 − 2g − 3

The arithmetic sequence a_ia i a, start subscript, i, end subscript is defined by the formula: a_1 = 15a 1 =15a, start subsc

daser333 [38]

Answer:

-1,512,390

Step-by-step explanation:

Given

a1 = 15

$a_i = a_{i-1} -7$

Let us generate the first three terms of the sequence

$a_2 = a_{2-1}-7\\a_2 = a_1 - 7\\a_2 = 15-7\\a_2 = 8$

For $a_3$

$a_3 = a_{3-1}-7\\a_3 = a_2 - 7\\a_3 = 8-7\\a_3 = 1$

Hence the first three terms ae 15, 8, 1...

This sequence forms an arithmetic progression with;

first term a = 15

common difference d = 8 - 15 = - -8 = -7

n is the number of terms = 660 (since we are looking for the sum of the first 660 terms)

Using the formula;

$S_n = \frac{n}{2}[2a + (n-1)d]\\$

Substitute the given values;

$S_{660} = \frac{660}{2}[2(15) + (660-1)(-7)]\\S_{660} = 330[30 + (659)(-7)]\\S_{660} = 330[30 -4613]\\S_{660} = 330[-4583]\\S_{660} = -1,512,390$

Hence the sum of the first 660 terms of the sequence is -1,512,390

6 0

3 years ago

A line passing through the points (-3,1) and (-2,t) has a slope equal to 2. Find the value of t.

Setler [38]

Step-by-step explanation:

BRAINLY FREE POINTS JSJJSJJ

7 0

3 years ago

Read 2 more answers

Look at the function f(x)=x^2-2. Which of the following describes the domain and range of the function and its inverse?

anygoal [31]

Answer:

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

6 0

4 years ago

What is the lcm of 44 36

laiz [17]

Answer:

396

Step-by-step explanation:

First, find the prime factorization of each number.

44 = 2^2 * 11

36 = 2^2 * 3^2

For the LCM, you need non-common factors and common factors with the larger exponent. Then you multiply together all the factors you use.

2 is a common factor. Both numbers have 2^2, so choose 2^2.

3 is not common. Use 3^2.

11 is not common. Use 11.

LCM = 2^2 * 3^2 * 11 = 396

8 0

3 years ago

Write the expression in interval notation

Ludmilka [50]

If we have a less than (or less than or equal to) sign with an absolute value, that indicates a conjunction where values can be expressed as an interval. The absolute value will be less than the number to the right, but it will also at the same time be greater than the negative of the number to the right. Don't forget that absolute value is a distance measurement, and the distance from the origin to -4 is 4 units, just like the distance from the origin to +4 is 4 units. Our particular absolute value will look like this: $\left[\begin{array}{ccc}x-6\end{array}\right] \leq 4$ and $\left[\begin{array}{ccc}x-6\end{array}\right] \geq -4$ . Solving the first absolute value we have that $x \leq 10$ and the second one is $x \geq 2$ . In interval notation we need to put x between the 2 inequality signs, which will look like this: $2 \leq x \leq 10$ . And there you go!

3 0

3 years ago