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3 years ago

The sequence {an } is defined by a of o = 1 and a of n + 1 = 2 a of n + 2 for n = 0, 1, 2.... What is the value of a of 3?

1 answer:

3 0

$\begin{cases}a(0)=1\\a(n+1)=2a(n)+2&\text{for }n\ge0\end{cases}$

Use the second part of the definition (the recursive one):

$a(1)=2a(0)+2=4$
$a(2)=2a(1)+2=10$
$a(3)=2a(2)+2=22$

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4 years ago

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Kazeer [188]

$n = 0$

Step-by-step explanation:

<h2>Factor the expression</h2>

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3 years ago

Give the solution set for the inequality 7x < 7(x - 2) in interval notation.

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ANSWER:

The solution set for the inequality 7x < 7(x - 2) is null set $\varnothing$

SOLUTION:

Given, inequality expression is 7x < 7 × (x – 2)

We have to give the solution set for above inequality expression in the interval notation form.

Now, let us solve the inequality expression for x.

Then, 7x < 7 × (x – 2)

7x < 7 × x – 2 × 7

7x < 7x – 14

7x – (7x – 14) < 0

7x – 7x + 14 < 0

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Which is false, so there exists no solution for x which can satisfy the given equation.

So, the interval solution for given inequality will be null set

Hence, the solution set is $\varnothing$

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4 years ago

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