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4 years ago

What is the recursive rule for the sequence? 3, −1, 1/3, −1/9, ...

Mathematics

2 answers:

Hunter-Best [27]4 years ago

7 0

Answer:

Step-by-step explanation:

(-1/9) /(1/3) = (1/3)/(-1) = -1/3....the common ratio of geometric sequence

the recursive rule is :

the nth term is : An =A1 × r^(n-1)

r : the common ratio

A1 ; the first term

r = -1/3 and A1 = 3

An =3 ×(-1/3)^(n-1)

laila [671]4 years ago

6 0

$\displaystyle a_1=-3\\r=-\dfrac{1}{3}\\a_n=a_{n-1}\cdot \left(-\dfrac{1}{3}\right)=-\dfrac{1}{3}a_{n-1}\\\\\\{\begin{cases}a_1=-3\\a_n=-\dfrac{1}{3}a_{n-1}\end{cases}}$

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Solve 26×6 using distributive

Cerrena [4.2K]

Answer:

Step-by-step explanation:first use parenthisis to seperate it and make it eisier to solve..sorry if my spelling is bad..

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3 years ago

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Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 244 meters

MissTica

We know that

[perimeter of rectangle]=2*(length+width)

Let
x-----------> length
y-----------> width
so
P=2*(x+y)-----------> 244=2*(x+y)-----> x+y=122-------> y=122-x

Area=x*y-------> x*(122-x)----> 122x-x²

find the derivative function and equals to zero

122-2x=0-----> 122=2x----------> x=61 m
y=122-x------> y=122-61---------> y=61 m

the maximum area is given by a square

the answer is
is a square of side 61 m

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4 years ago

Write the first three terms in the following sequences. Identify them as arithmetic or geometric

vaieri [72.5K]

Answer:

$A(1)=9$

$A(2)=4$

$A(3)=-1$

Arithmetic sequence

Step-by-step explanation:

We are given that

$A(n+1)=A(n)-5 \;for\;n\geq 1$ A(1)=9

We have to find first three terms and identify the sequence is geometric or arithmetic.

Substitute n=1

Then, we get

$A(2)=A(1)-5=9-5=4$

For n=2

$A(3)=A(2)-5=4-5=-1$

For n=3

$A(4)=-1-5=-6$

$d_1=A_2-A_1=4-9=-5$

$d_2=A_3-A_2=-1-4=-5$

$d_3=A_4-A_3=-6+1=-5$

$d_1=d_2=d_3=-5$

When the difference of consecutive terms are constant then the sequence is arithmetic sequence.

Therefore, given sequence is arithmetic sequence.

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3 years ago

Convert the following: 110110two to base ten 25ten to base two

blagie [28]

Answer:

110110 in base 2 when converted in base 10 will be equal to 54
25 in base 10 is equal to 1001 base 2

Step-by-step explanation:

Part 1: 110110two to base ten

For conversion from base 2 to base 10 we multiply each digits of given number with powers of 2

$=1*2^5 + 1 * 2^4 + 0 * 2^3 + 1 *2^2 + 1* 2^1 + 0*2^0\\ =1*32+ 1* 16 + 0 + 1*4 + 1*2 +0\\ =32 + 16 +4 + 2\\ = 54$

So 110110two when converted in base 10 will be equal to 54

Part 2: 25ten to base two

For conversion from base 10 to base 2 we will divide the given number with 2 repeatedly and store the remainders until the quotient comes 1. The solution is as follows:

25/2 = 12 remainder 1

12/2 = 6 remainder 0

6/2 = 3 remainder 0

3/2 = 1 remainder 1

Now the remainders will be written in inverse order as:

=1001 base 2

So 25 in base 10 is equal to 1001 base 2

I hope it will help you!

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4 years ago

1. Five gallons of lemonade cost $8.00, which is a rate of _____per____.

Hitman42 [59]

Answer:

1. $1.60

2. gallon

Step-by-step explanation:

Each gallon of lemonade would cost $1.60.

The rate is $1.60 per gallon.

Hope it helps!

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4 years ago

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