What are the next two terms in the sequence - 16, 4, - 1, 1/4

Answer: fifth term = - 1/16

Sixth term = 1/256

Step-by-step explanation:

The given sequence is a geometric progression. This is because the ratio of two consecutive terms is constant.

We will apply the formula for determining the nth term of a geometric progression series.

Tn = ar^n-1

Where

Tn = value of the nth term of the geometric series

a = The first term of the series.

r = common ratio (ratio of a term to a consecutive previous term)

n = number of terms in the series

From the in information given,

a = - 16

r = 4/-16 = - 1/4

The next 2 terms are the 5th and 6th terms.

T5 = - 16 * - 1/4^ (5-1)

T5 = - 16 * (-1/4) ^4

T5 = - 16 * 1/256 = - 1/16

The 6th term would be the 5th term * the common ratio. It becomes

T6 = - 1/16 * -1/4 = 1/256