Answer:
In year 2039 both the events will happen again.
Step-by-step explanation:
We are given the following in the question:
Family reunion:
Every 7 year
Update the family tree:
Every 6 years
1997 was the year when they had a family reunion as well as they updated their family tree.
We have to find the year in which both the events will occur together.
We find the lowest common multiple of 7 and 6.

Thus, after 42 years both the event will happen again.
Year:

Thus, in year 2039 both the events will happen again.
All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If

is the component for state

, then you have

which means

. So the state vector is

.
Your answer will be A. (8,1)
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