Question

The general term of a sequence is given by a = 51 +3(n-10), where a0 is the initial value. Which of the following expressions also gives the general term of the sequence?

A) 10+ 3(51-n)
B) 17+ 3n
C) 21+ 3n
D) 51-3(-10)

Answer 1

The correct expressions that give the general term of the sequence are B) 17+ 3n and C) 21+ 3n, as both simplify to match the original sequence definition.

Step-by-step explanation:

The student's question is about finding an expression that also gives the general term of the sequence defined by a = 51 +3(n-10). To find an equivalent expression, we must simplify or modify the given formula without changing its overall value for any term in the sequence.

Looking at the options provided:

• A) 10+ 3(51-n) does not simplify to the given expression.
• B) 17+ 3n is equivalent since if you distribute 3(n-10), you get 3n - 30. Adding 51 to -30 gives 21, so the expression simplifies to 21 + 3n, which simplifies to the given term.
• C) 21+ 3n is exactly what we get when we simplify the given term, so this is a correct answer.
• D) 51-3(-10) does not represent a general term since it lacks the variable n and thus cannot account for changing values in the sequence.

Therefore, the correct options that give the general term of the sequence are B) 17+ 3n and C) 21+ 3n.

Answer 2

The general term of the sequence is a = 51 + 3(n-10), which simplifies to a = 3n + 21. The expression B) 17 + 3n also gives the general term of the sequence.

Step-by-step explanation:

The general term of the sequence is given by a = 51 + 3(n-10), where a0 is the initial value.

To determine which of the given expressions also gives the general term of the sequence, we can start by simplifying the expression a = 51 + 3(n-10).

Expanding the expression gives a = 51 + 3n - 30, which can be simplified to a = 3n + 21.

Comparing this with the options, we can see that the expression B) 17 + 3n also gives the general term of the sequence.