Explanation:
1).
To find the common difference of the sequence subtract the previous term from the next term
That's
d = 9 - 5 = 4 or
d = 13 - 9 = 4 or
d = 17 - 13 = 4
Since it's the same for any of the terms chosen
The common difference = 4
2).
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 5
d = 4
We have
A(n) = 5 + ( n - 1)4
= 5 + 4n - 4
= 4n + 5 - 4
We have the answer as
A(n) = 4n + 1
3).
To find the 25th term substitute the value of n that's 25 into the formula
We have
A(25) = 4(25) + 1
= 100 + 1
We have the final answer as
A(25) = 101
Hope this helps you