Question

Find the 10th term of the geometric sequence 8, -24, 72, ...

Answer 1

The 10th term of the geometric sequence 8, -24, 72, ... is -157464, found by using the geometric sequence formula with the common ratio of -3.

Step-by-step explanation:

Finding the 10th Term of a Geometric Sequence

To find the 10th term of the geometric sequence 8, -24, 72, ..., we must identify the common ratio (r) and use the formula for the nth term of a geometric sequence, which is given by Tn = a*r(n-1), where 'a' is the first term and 'n' is the term number.

First step, identify the common ratio (r) by dividing the second term by the first term: r = -24/8 = -3.

Now, using the formula with a = 8, r = -3, and n = 10, we get:

T10 = 8 * (-3)(10-1) = 8 * (-3)9.

To calculate (-3)9, we understand that it's a negative number raised to an odd power, so the result will be negative. The magnitude is 39, which is 19683. Thus, T10 = 8 * (-19683) = -157464.

The 10th term of the sequence is -157464.

Answer 2

-157464

Step-by-step explanation:

Geometric Sequence formula = ar^n-1

In the above formula,

a = the first term

r = common differnce

n = the term which we want to know

So, the first term is 8.

We can tell that these numbers have a common difference of -3.

We need to find the 10th term.

=> 8*(-3^10-1)

=>8*-3^9

=>8*-19683

=>-157464