Question

Which formula can be used to describe the sequence? -2 2/3,-5 1/3,-10 2/3,-21 1/3,-42 2/3

Answer 1

Answer:

Xn = -8/3(2)^n-1

Step-by-step explanation:

Given Which formula can be used to describe the sequence? -2 2/3,-5 1/3,-10 2/3,-21 1/3,-42 2/3

So the sequence can be converted as

- 8/3 , - 16/3 , - 32/3, - 64/3, - 128/3

here we know that the sequence is obtained by multiplying the next number by 2.

Thus the given sequence is in geometric progression or G.P.

We know that in a GP each term is got after multiplying the constant term to the next number.

So the formula can be used as Xn = ar^n-1

                                             Xn = -8/3(2)^n-1

Answer 2

Answer:

A(n) = - 8/3 × 2^n - 1

Step-by-step explanation:

We begin by writing the sequence in improper fraction form.

We have :

-8/3, - 16/3, - 32/3, - 64/3, - 128/3

This is a geometric sequence whose common ratio is 2

We therefore need to look for a formula that will fit the sequence.

The nth term of a geometric progression is given by :

An = ar^n-1

In our case :

a = - 8/3

r = 2

We do the substitution to get :

A(n) = - 8/3 × 2^n - 1