Geometric Sequence

Question

find the two missing terms between 128 and -2

Answer 1

A geometric sequence is a series of numbers where the next term is multiplied by a specific factor.

Writing the whole sequence you can see what I mean.

You can also write the missing terms as 128, 128 *n, 128*n², 128*n³ = -2

So we can see

128*n³ = -2

n³ = -2/128

n³ = -1/64

taking the cubed root

n = -1/4 (The negative stays when taking an odd root)

So you multiply 128 by -1/4 to get the next term

128*-1/4 = -32

The next term is -32*-1/4 = 8

Then to check for the last term

8 * -1/4 = -2

So the factor is -1/4 and the total sequence is

128, -32, 8, -2 (Notice that the terms alternate from positive to negative)

Answer 2

need to find ratio parameter (r)

128 is first term and -2 is 4th term

Using formula for nth term of a geometric sequence: a(n) = a(1) * r^(n-1)

a(4) = a(1) * r^3

-2 = 128 * r^3

-1/64 = r^3

-1/4 = r

So 2nd term is 128 * -1/4 = -32

and 3rd term is -32 * -1/4 = 8

Answer 3

Because of the alternating sign, we know that our common ratio is negative. Since we have 2 missing terms, we know that:

128 = (-2)r^{n - 1} = -2r³

-64 = r³

r = -4

Therefore, since the common ratio is -4, our first missing term is -2(-4) = 8, and our second missing term is 8(-4) = -32.