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postnew [5]
3 years ago
5

The formula for any geometric sequence is an = a1 · rn - 1, where an represents the value of the nth term, a1 represents the val

ue of the first term, r represents the common ratio, and n represents the term number. What is the formula for the geometric sequence 1, -2, 4, -8, ...? an = 1 · (-2)n - 1 an = -2 · 1n - 1 an = -8 · (-2)n - 1 an = 1 · 2n - 1
Mathematics
2 answers:
kati45 [8]3 years ago
6 0

Answer:

\huge\boxed{a_n=1\cdot(-2)^{n-1}}

Step-by-step explanation:

a_n=a_1r^{n-1}

We have the geometric sequence: 1, -2, 4, -8, ...

Find the common ratio:

r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}

a_1=1,\ a_2=-2

substitute:

r=\dfrac{-2}{1}=-2

Substitute

a_1=1;\ r=-1

to

a_n=a_1r^{n-1}

a_n=1\cdot(-2)^{n-1}

Nuetrik [128]3 years ago
6 0

Answer:

a_{n}=1 (-2)^{n-1}

Step-by-step explanation:

Hi there!

Let's do it,

1)1,-2,4,-8  

First let's find the q, the common ratio by dividing the second term by the anterior one.

-2:1 =-2

4:-2=-2

So the common ratio is -2. Plugging in on the General formula:

a_{n}=a_{1}q^{n-1}

a_{n}=1 (-2)^{n-1}

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