<u>3x + 2y = 4</u>

Here are a few different ways
to represent the same line:

2y = 4 - 3x

y = -1.5x + 2

5y = -7.5x + 10

3x = 4 - 2y

x = -2/3y + 4/3

7 0

3 years ago

a 1 =− 3 1 a, start subscript, 1, end subscript, equals, minus, start fraction, 1, divided by, 3, end fraction a i = a i − 1

MrRa [10]

Answer:

$S_{75}=-506.888989761$ X 10^{32}$

Step-by-step explanation:

Given the sequence

$a_1=-\dfrac{1}{3}\\ a_i=a_{i-1}\cdot (-3)$

$a_2=a_{2-1}\cdot (-3)=a_1 \cdot (-3) = -\dfrac{1}{3}\cdot (-3)=1\\a_3=a_{3-1}\cdot (-3)=a_2 \cdot (-3) = 1 \cdot (-3)=-3\\a_4=a_{4-1}\cdot (-3)=a_3 \cdot (-3) = -3 \cdot (-3)=9\\$

Therefore the sequence is:

$-\dfrac{1}{3}, 1, -3, 9, ...$

This is a geometric sequence where the:

First Term, $a_1=-\dfrac{1}{3}$

Common ratio, r =-3

We want to determine the sum of the first 75 terms.

For a geometric sequence, the sum:

$S_n=\dfrac{a_1(1-r^n)}{1-r} \\$

Therefore:

$S_{75}=\dfrac{-\dfrac{1}{3}(1-(-3)^{75})}{1-(-3)} \\\\=\dfrac{-(1-(-3)^{75})}{4*3}\\\\S_{75}=\dfrac{(-3)^{75}-1}{12}\\\\S_{75}=-506.888989761$ X 10^{32}$

5 0

3 years ago