Answer:
a. 3 (see below for explanation)
b. Ln = 4 + 3(n -1)
c. 48
d. dn = 6n +2
Explanation:
a. The common difference is found by subtracting any given term from the next one: 7 -4 = 3, or 10 -7 = 3. The common difference is 3.
__
b. The general expression for an arithmetic sequence with first term a1 and common difference d is ...
an = a1 + d(n -1)
Here, the first term is 4 and the common difference is d. We choose to name the n-th term of Levy's sequence "Ln", so we can fill in the numbers to get ...
Ln = 4 + 3(n -1)
__
c. We can call the terms of Zack's sequence Zn, so we have ...
Zn = 3·Ln = 3·(4 + 3(n -1)) = 12 +9(n -1)
Putting 5 where n is in this equation, we find ...
Z5 = 12 +9(5 -1) = 48
The 5th term of Zack's sequence is 48.
__
d. The difference of n-th terms of the two sequences is ...
dn = Zn -Ln = (3·Ln) - Ln = 2Ln = 2(4 +3(n -1)) = 8 +6(n -1)
dn = 6n +2