Question

Identify the 16th term of a geometric sequence where a1 = 4 and a8 = −8,748.

Answer 1

To find the 16th term of a geometric sequence, divide the 8th term by the 1st term to determine the common ratio. Then, use the formula an = a1 * r^(n-1), where an is the nth term, a1 is the 1st term, and r is the common ratio, to find the 16th term.

Step-by-step explanation:

To find the 16th term of a geometric sequence, we need to determine the common ratio (r) of the sequence. We can do this by dividing the 8th term (-8,748) by the 1st term (4):

r = a8/a1 = -8,748/4 = -2,187

Now, we can use the formula to find the nth term of a geometric sequence:

an = a1 * r^(n-1)

Substituting the values, we get:

a16 = 4 * (-2,187)^(16-1) = 4 * (-2,187)^15

Calculating this value will give us the 16th term of the sequence.

Answer 2

Step-by-step explanation:

The formula used to determine the terms is

an = a1 × rn - 1

It is given that

a1 = 4

a8 = -8,748

Substituting the values in the formula

-8748 = 4 × r8 - 1

r7 = -8748/4

r7 = -2187

r = -3

So the 16th term is

a16 = 4 × 316-1

a16 = -57395628

Therefore, the 16th term is -57395628.