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Consider the sequences
a. ${a_{n}} = {- 2, 5, 12, 19, \dots}$
b. ${b_{n}} = {3, 6, 12, 24, 48, \dots}$
(a) Find the next two terms of the sequence.
(b) Find a recurrence relation that generates the sequence.
(c) Find an explicit formula for the nth term of the sequence.

Kamren Franco 2022-01-23

Please, solve for the values of x for each of the following exponential equations and inequalities.
(a) $8^{2 - x} = 2$
(b) ${(\frac{1}{2})}^{x} < (\frac{1}{8})$
(c) $5^{x} = 25^{x - 2}$
(d) $3^{x + 2} \geq 27$
(e) $4^{3 x} = 8^{x - 1}$

Vilharjevw7 2022-01-23

Find $a_{5}$ and $a_{n}$ for the geometric sequence.
$a_{3} = 2$ , $r = \frac{1}{3}$

Mlejd5 2022-01-23

Prove, using the definitio of a convergent sequence
$lim_{n \to \infty} \ln ({\frac{n}{n + 1}}) = 0$

logosomatw 2022-01-23

Use the approach in Gausss

Adrian Cervantes 2022-01-23

Find the limits of the following sequences
$a_{n} = n^{\frac{5}{n}}$

Lainey Goodwin 2022-01-23

Give an example of such $f (x)$ and prove, why it works
A non constant function $f : [0, 1] \to R$ such that $f (x) \geq 0$ for any $x \in [0, 1]$ , but $\int_{0}^{1} f (x) d x = 0$

Jazmin Perry 2022-01-23

We have the sequence $1, 2, 3, 5, 8$
What is the next number in the sequence?

Connor Randall 2022-01-23

For each of the sequences, write a formula for the general term. Use the formula to find $a_{20}$
1) $2, 7, 12, 17, \dots$
2) $6, 1, - 1, - 9, \dots$
3) $a_{0} = 4, d = - 0.3$
4) $a_{0} = \frac{3}{4}, d = - \frac{1}{4}$

Reese Munoz 2022-01-23

Give the first six terms of the following sequences.
1) $g_{1} = 2$ and $g_{2} = 1$
2) $c_{1} = 4, c_{2} = 5$ and $c_{n} = c_{n - 1} \times c_{n - 2}$ for $n \geq 3$
3) $b_{1} = 1, b_{2} = 3$ and $b_{n} = b_{n - 1} - b_{n - 2}$ for $n \geq 3$
4) $d_{1} = 1, d_{2} = 1$ and $d_{n} = {(d_{n - 1})}^{2} + d_{n - 2}$ for $n \geq 3$

Arely Briggs 2022-01-23

How do you use algebra to solve $(x - 1) (x + 2) = 18$ ?

2alr8w 2022-01-23

Find the ﬁrst four terms of each of the recursively deﬁned sequences
$d_{k} = k {(d_{k - 1})}^{2}$ for all integers $k \geq 1$
$d_{0} = 3$

tripplek7i 2022-01-23

Show that the following sequences converge
$a_{n} = 5 + \frac{1}{n}$

Jessie Jenkins 2022-01-23

Find the Z transform of the sequence
$3^{k} + {(- 3)}^{k} + 3 k$

Keaton Good 2022-01-23

How many sequences can be formed using all the letters in ARCANSAS?

David Rojas 2022-01-23

Solve the sequece, please
a) $\frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, ?, ?$
b) $1, 3, 6, 10, 15, 21, ?, ?$
c) $1, 4, 9, 16, 25, 36, ?, ?$
d) $1, 2, 4, 8, 16, 32, ?, ?$

Keaton Good 2022-01-23

If a die is rolled 30 times, there are $6^{30}$ different sequences possible.
What fraction of these sequences have exactly eight 1s and eight 6s?

Advadlippabrj 2022-01-23

Let ${x_{n}}_{n = 1}^{\infty}$ , and ${y_{n}}_{n = 1}^{\infty}$ be two sequences of positive numbers. Assume that $x_{n} ⟨ y_{n}$
For each one of the following claims, decide whether they are always true, always false, or sometimes true and sometimes false (depending on the specific sequences) and prove it.
1) $x_{n} ⟨ \frac{x_{n} + y_{n}}{2}$
2) $\frac{x_{n} + y_{n}}{2} ⟨ y_{n}$

Ahmed Stewart 2022-01-23

A coin is tossed 7 times and the sequence of heads and tails are observed. So, how many different sequences have at least 3 heads?

Caroline Elliott 2022-01-23

Let $(a_{n})$ , $(b_{n})$ be two bounded sequences.
a.Show that $lim_{n \to \infty} \supset max (a_{n}, b_{n}) \geq max (lim_{n \to \infty} \supset a_{n}, lim_{n \to \infty} \supset b_{n})$ .
b. Give an example of $(a_{n}), (b_{n})$ such that the strict inequality holds.

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