Let's analyze the problem to determine which statement is NOT true based on the sequences provided:

Sequence A:

• $a_1 = 5$
• $a_n = a_{n-1} + 20$

This is an arithmetic sequence because the next term is obtained by adding 20 to the previous term. The common difference $d$ is 20.

The general form of an arithmetic sequence is: $a_n = a_1 + (n-1) \cdot d$ Substituting the values for $a_1 = 5$ and $d = 20$: $a_n = 5 + (n-1) \cdot 20 = 20n - 15$

Sequence B:

• $a_1 = 7$
• $a_n = 5a_{n-1}$

This is a geometric sequence because each term is obtained by multiplying the previous term by 5. The common ratio $r$ is 5.

The general form of a geometric sequence is: $a_n = a_1 \cdot r^{n-1}$ Substituting the values for $a_1 = 7$ and $r = 5$: $a_n = 7 \cdot 5^{n-1}$

Let's now review the given statements:

1. "Sequence B can be represented by $a_n = 7 \cdot 5^{n-1}$"
   This is true, as shown in the formula above for a geometric sequence.

2. "The common ratio of sequence B is 5."
   This is also true, as the common ratio in a geometric sequence is 5.

3. "The common difference of sequence A is 20."
   True, since Sequence A is arithmetic with a common difference of 20.

4. "Sequence A can be represented by $a(n) = 20n + 5$"
   This is NOT true. The correct formula for Sequence A is $a_n = 20n - 15$, not $20n + 5$.

Conclusion:

The incorrect statement is the last one:

• "Sequence A can be represented by $a(n) = 20n + 5$".

Would you like further details or have any questions about this explanation? Here are five related questions to expand your understanding:

1. How can you derive the general form of an arithmetic sequence?
2. What makes a sequence geometric versus arithmetic?
3. Can a sequence be both arithmetic and geometric?
4. What are some real-life applications of geometric sequences?
5. How would you solve for a specific term in either sequence?

Tip: Always double-check whether a sequence is arithmetic or geometric before applying formulas.