Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The terms of the sequence are:

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

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:

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

$a_8=(x+3)(-2x)^{7}$

$a_8=-128x^7(x+3)$

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