Answer :
The correct formula to determine the nth term of the arithmetic sequence given is D f(n) = 6 + 9n. This is derived using the formula for an arithmetic sequence's nth term which is a1 plus the product of (n - 1) and the common difference.
Finding the nth Term of an Arithmetic Sequence
To determine the nth term of an arithmetic sequence, we can use the formula f(n) = a1 + (n-1)d, where a1 is the first term and d is the common difference. Looking at the given sequence 6, 15, 24, 33, 42, we can see that the first term a1 is 6, and the common difference d is 9 because 15 - 6 = 9, 24 - 15 = 9, and so on. Plugging these values into the formula, we get:
f(n) = 6 + (n-1) times 9
This simplifies to:
f(n) = 6 + 9n - 9
Which further simplifies to:
f(n) = 6 + 9(n - 1)
Therefore, the correct answer is:
D f(n) = 6 + 9n
The formula for the nth term of the arithmetic sequence is 3(3n-1) or -3+9n(option B)
What is arithmetic sequence?
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
The nth term of a n arithmetic sequence is given as:
a(n) = a+(n-1)d
where a is the first term and d is the common difference
a = 6
d = 15-6 = 9
a(n) = 6+( n-1) 9
= 6+9n -9
a(n) = 9n-3
a(n) = 3(3n-1)
therefore the formula for the nth term of the sequence is 3(3n-1)
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