Question

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

Answer 1

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