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Math  /  Algebra

QuestionWrite an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n=1 for the first term. −6,−12,−18,−24,…an=□\begin{array}{l} -6,-12,-18,-24, \ldots \\ a_{n}=\square \end{array}

Studdy Solution

STEP 1

1. The sequence provided is an arithmetic sequence where each term is derived by adding a constant difference to the previous term.
2. The first term of the sequence can be denoted by a1a_1.
3. The common difference between consecutive terms is consistent throughout the sequence.
4. The general term of an arithmetic sequence can be written in the form an=a1+(n−1)da_n = a_1 + (n-1)d, where dd is the common difference and a1a_1 is the first term.

STEP 2

1. Identify the first term a1a_1 of the sequence.
2. Determine the common difference dd.
3. Write the general formula for the nn-th term of the arithmetic sequence.
4. Substitute the values of a1a_1 and dd into the general formula.

STEP 3

Identify the first term a1a_1 of the sequence.
Given sequence: −6,−12,−18,−24,… -6, -12, -18, -24, \ldots
The first term is: a1=−6 a_1 = -6

STEP 4

Determine the common difference dd between consecutive terms.
Difference between the first two terms: −12−(−6)=−12+6=−6 -12 - (-6) = -12 + 6 = -6
The common difference is: d=−6 d = -6

STEP 5

Write the general formula for the nn-th term of the arithmetic sequence.
The general formula for an arithmetic sequence is: an=a1+(n−1)d a_n = a_1 + (n-1)d

STEP 6

Substitute the values of a1a_1 and dd into the general formula.
an=−6+(n−1)(−6) a_n = -6 + (n-1)(-6)
Simplify the expression: an=−6−6(n−1) a_n = -6 - 6(n-1) an=−6−6n+6 a_n = -6 - 6n + 6 an=−6n a_n = -6n
The general term of the sequence is: an=−6n a_n = -6n

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