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

Mathematics

2 answers:

Hunter-Best [27]3 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]3 years ago

6 0

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

You might be interested in

there is a college student who wants to buy apples from the local store. the store generally sells about 5 apples for every 2 cu

myrzilka [38]

125 apples sold after 6 hours

3 0

2 years ago

In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

Maksim231197 [3]

Answer:

See explanation

Step-by-step explanation:

Let $x,\ x\ge 0$ be the number of students and $y,\ y\ge 0$ be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

$15x+25y\ge 3,750$

2. The auditorium can accommodate up to 180 spectators, hence

$x+y\le 180$

3. We get the system of inequalities:

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.$

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise $\$(15\cdot 50+25\cdot 125)=\$3,875$