Question

Find the 7th term in the sequence -1, -3, -9,...

Answer 1

Answer:

The answer is 729

Step-by-step explanation:

to get the next term, the sequence multiples the previous number by -3

1 * -3 = -3

-3 * -3 = 9

and so on.

To get the 7th term:

-27 * -3 = 81 (5th term)

81 * -3 = -243 (6th)

-243 * -3 = 729 (7th)

Answer 2

Answer:

-729

Step-by-step explanation:

First, note that the sequence is increasing not linearly. Thus, this is a geometric sequence.

The explicit formula for a geometric sequence is:

$x_n=a(r)^{n-1}$

Where a is the first term, r is the common ratio, and n denote the nth term.

So, from the sequence, we can see that the first term a is -1.

Also, each subsequent term is 3 times that of the previous one. In other words, the common ratio r is 3.

Thus, substituting:

$x_n=-(3)^{n-1}$

So, to find the 7th term, substitute n for 7:

$x_7=-(3)^{7-1}$

Simplify:

$x_7=-(3)^6\\x_7=-729$

And that's our answer :)