Find an arithmetic sequence with a common difference of -5

Gavyn Whitehead
2022-09-14
Answered

Find an arithmetic sequence with a common difference of -5

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Find the fourth term in the following recursively defined sequence given ${a}_{1}=4$ and ${a}_{n}={a}_{n-1}+2$

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Prove:

$\underset{n\to \mathrm{\infty}}{lim}\mathrm{ln}\left(\frac{n+1}{n}\right)=0$

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Find $a}_{5$ and $a}_{n$ for the geometric sequence.

${a}_{3}=2$ , $r=\frac{1}{3}$

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Identify the sequences as arithmetic or geometric.

a. 2, 6, 18, 54, 162

b. 1, 8 ,15, 22, 29

c. 11, 15, 19, 23, 27

a. 2, 6, 18, 54, 162

b. 1, 8 ,15, 22, 29

c. 11, 15, 19, 23, 27

asked 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 $n\ge 3$

3)${b}_{1}=1,{b}_{2}=3$ and $b}_{n}={b}_{n-1}-{b}_{n-2$ for $n\ge 3$

4)${d}_{1}=1,{d}_{2}=1$ and $d}_{n}={\left({d}_{n-1}\right)}^{2}+{d}_{n-2$ for $n\ge 3$

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asked 2022-04-15

Find the following sums of arithmetic sequences.

$881+872+863+854+\dots .8$

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Find the limit of the sequence

$a}_{n}=\frac{5{n}^{2}-8n+11}{7n+4$