How do you write the first five terms of the geometric sequence $a_1=5, a_(k+1)=-2a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?

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How do you write the first five terms of the geometric sequence $a_1=5, a_(k+1)=-2a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?

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Answer 1 · 2017-09-29T08:48:22

first 5 terms

${5,-10,20,-40,80}$

common ratio

$r=-2$

nth term

$a_n=5(-2)^(n-1)$

Explanation:

$a_1=5$

$a_(k+1)=-2a_k$

$a_1=5$

$a_2=-2a_1=-2xx5=-10$

$a_3=-2a_2=-2xx-10=20$

$a_4--2a_3=-2xx20=-40$

$a_5=-2a_4=-2xx-40=80$

first 5 terms

${5,-10,20,-40,80}$

common ratio

is $a_(k+1)/a_k=(-2a_k)/a_k$

$r=-2$

nth term of any Gp

$a_n=a_1r^(n-1)$

$a_n=5(-2)^(n-1)$

Answer 2 · 2017-10-08T10:11:11

$a_1 = 5$ and $a_(k + 1) = -2a_k$

so, $a_2 = -2a_1$

=> $a_2 = -10$

Also, $a_3 = -2a_2$

i.e. $a_3 = 20$

so, our terms are $5, -10, 20, -40,...$

Hence, 1st term 5 and common ratio -2

Now, nth term is $ar^(n - 1)$

i.e. $5(-2)^(n - 1))$

or, $(-5/2)(-2^n)$

With n = 7 we have:

$(-5/2)(-2^7) = 320$

:)>

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How do you write the first five terms of the geometric sequence $a_1=5, a_(k+1)=-2a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?

2 Answers

Explanation:

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Science

Math

Humanities

... and beyond

How do you write the first five terms of the geometric sequence a_1=5, a_(k+1)=-2a_ka_1=5, a_(k+1)=-2a_k and determine the common ratio and write the nth term of the sequence as a function of n?

2 Answers

Explanation:

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Impact of this question

How do you write the first five terms of the geometric sequence $a_1=5, a_(k+1)=-2a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?