Answer:
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Given:
The sequence is:
To find:
The explicit formula for the given sequence then find the 47th term.
Solution:
We have,
The difference between two consecutive terms are:
The given sequence has a common difference. So, the given sequence is an arithmetic sequence with first term -3 and common difference 8.
The explicit formula for an arithmetic sequence is:
Where, a is the first term and d is the common difference.
Putting and in the above formula, we get
Putting , we get
Therefore, the explicit formula for the given sequence is and the 47th term is 365.
Answer:
Option D. 13122 is the answer.
Step-by-step explanation:
As we can see from the table having interval and average rate of change, figures under average rate of change are forming a geometric sequence.
Sequence is 2, 6, 18 , 54, 162, 486.
and we have to find the average rate of change from x = 8 to x = 9, means we have to find 9th term of the given sequence.
Now we know that explicit formula of the sequence can be written as
where Tn is the nth term of the sequence.
a = first term
r = common ratio
n = number of the term
Now from this explicit formula we can find the 9th term of the sequence.
From the given table
a = 2, r = 3, n = 9
T9 = 13122
Therefore Option D. 13122 will be the answer.