Slovenujozk
2022-09-14
Answered

Find the explicit formula for the following sequence 2, 4, 6, 8,...

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asked 2022-09-26

Find the 30th term of the arithmetic series 2, 5, 8, …

asked 2022-03-22

Let $a}_{1},{b}_{1$ be two real numbers such that $0<{a}_{1}<{b}_{1}$. For $n\ge 1$, we define $a}_{n+1}={\left({a}_{n}{b}_{n}\right)}^{\frac{1}{2}$ and ${b}_{n+1}=\frac{({a}_{n}+{b}_{n})}{2}$

a) Prove that the sequence $\left\{{a}_{n}\right\}n\in N$ is monotonically increasing and that the sequence $\left\{{b}_{n}\right\}n\in N$ is monotonically decreasing.

b) Show that the sequences $\left\{{a}_{n}\right\}$ and $\left\{{b}_{n}\right\}$ are bounded.

c) Deduce that the two sequences converge and prove that they converge to the same limit.

asked 2022-01-05

If a die is rolled 30 times, there are $6}^{30$ different sequences possible. The following question asks how many of these sequences satisfy certain conditions.

What fraction of these sequences have exactly three 3s and three 2s?

What fraction of these sequences have exactly three 3s and three 2s?

asked 2022-09-05

How do you find the first five terms given ${a}_{1}=-6$ and ${a}_{n+1}={a}_{n}+3$?

asked 2022-09-26

Fint 30th term of the arithmetic series 2, 5, 8, …

asked 2022-09-07

Find the explicit formula for the following sequence 12,24,48,...

asked 2022-06-03