4th option is correct: 16 R5
Given:
Arithmetic sequence -5, 13, 31, 49..........
We are to find the explicit formula of the sequence above. An explicit formula provides a binding formula for finding nth term.
To find the formula, we need to know the first term and the common difference.
The common difference is the difference between each successive terms of the sequence.
In the given sequence, the common difference is 18;
13-(-5) = 18
31 - 13 = 18
49 - 31 = 18
n calculation of the nth term
1 -5 -5 + 18(0) = -5
2 13 -5 + 18(1) = 13
3 31 -5 + 18(2) = 31
4 49 -5 + 18(3) = 49
Since the common difference is 18, we can now derive the formula;
b(n) = -5 + 18(n-1)
n is the position of the term
Any number in the sequence can be derived using the explicit formula
-5 + 18(n-1)
Answer:
The percentage change each year is 2%
Step-by-step explanation:
Generally, we can have an exponential equation written as;
f(t) = I( 1 + r)^t
where f(t) is the value at a certain time
I is the initial value at t = 0
r is the growth rate
t is the time we are looking at
Thus, we have it that;
1.02 = 1 + r
r = 1.02 -1
r = 0.02
So, let us write 0.02 as a percentage
We have this as 2/100 which is the same as 2%
The percentage change each year is 2%
