Write the first five terms of the geometric sequence $a}_{1}=64,{a}_{k+1}=\frac{1}{2}{a}_{k$ and determine the common ratio and write the nth term of the sequence as a function of n

mafalexpicsak
2022-10-16
Answered

Write the first five terms of the geometric sequence $a}_{1}=64,{a}_{k+1}=\frac{1}{2}{a}_{k$ and determine the common ratio and write the nth term of the sequence as a function of n

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Zackary Mack

Answered 2022-10-17
Author has **12** answers

First, it's better to change the sequence and write that in this way:

$a}_{k}=\frac{1}{2}{a}_{k-1$

It's obvious that each term is half of the previous term, and by the definition of geometric sequence, we can write the equation very simple.

is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number

$a}_{n}=64\times {\left(\frac{1}{2}\right)}^{n-1$

$a}_{k}=\frac{1}{2}{a}_{k-1$

It's obvious that each term is half of the previous term, and by the definition of geometric sequence, we can write the equation very simple.

is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number

$a}_{n}=64\times {\left(\frac{1}{2}\right)}^{n-1$

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List the first 10 terms of these sequences:

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1) The sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term

2) The sequence whose n-th term is the sum of the first n positive integers

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However, the number of terms in the sub sequence,

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Find the ${a}_{0},{a}_{1},{a}_{2}$ , and $lim{a}_{n}$ for the following sequences: $3\times 10=30$

1) ${a}_{n}=(7+3n)/(5-2n)$

2) ${a}_{n}=(8n)/(9-{n}^{2})$

3) ${a}_{n}=1/2{a}_{n}+8/{a}_{n}\text{}({a}_{0}=1\text{}given)$

1) ${a}_{n}=(7+3n)/(5-2n)$

2) ${a}_{n}=(8n)/(9-{n}^{2})$

3) ${a}_{n}=1/2{a}_{n}+8/{a}_{n}\text{}({a}_{0}=1\text{}given)$