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3 years ago

10

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 1, 3, 9, 27

, 81, …

1 answer:

Dmitry_Shevchenko [17]3 years ago

3 0

This is geometric with a common ratio of 3 (3/1 = 3 and 9/3 = 3 etc)
the formula for the nth term is
an = 3^(n-1)

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What is the eighth term in the sequence x+3, - 2x^2 - 6x, 4x^3 +12x^2

Anastasy [175]

Answer:

$a_8=-128x^8-384x^7$

Step-by-step explanation:

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$x+3,-2x^2-6x,4x^3+12x^2,...$

We can rewrite the terms in factored form to get;

$x+3,-2x(x+3),4x^2(x+3),...$

We can see that the subsequent terms are obtained by multiplying the previous term by $-2x$ . This is called the common ratio.

Therefore the first term of this geometric sequence is $a_1=x+3$ and the common ratio is $r=-2x$ .

The nth term of a geometric sequence is given by: $a_n=a_1(r^{n-1})$ .

Let us substitute the first term, the common ratio, and $n=8$ to obtain:

$a_8=(x+3)(-2x)^{8-1}$

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Step-by-step explanation:

...

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