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
