Questions: The first four terms of an arithmetic sequence are -11, -5, 1, 7. What is the equation for an? A an = -11(n-1)-6 B an = 6(n-1)-11 C an = -11(n-1)+6 D an = -6(n-1)-11

The first four terms of an arithmetic sequence are -11, -5, 1, 7. What is the equation for an? A an = -11(n-1)-6 B an = 6(n-1)-11 C an = -11(n-1)+6 D an = -6(n-1)-11
Transcript text: The first four terms of an arithmetic sequence are $-11,-5,1,7$. What is the equation for $a_{n}$ ? A $a_{n}=-11(n-1)-6$ B $a_{n}=6(n-1)-11$ C $a_{n}=-11(n-1)+6$ D $a_{n}=-6(n-1)-11$
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Solution

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Solution Steps

Step 1: Identify the first term and common difference

The first term of the arithmetic sequence is \( a_1 = -11 \).
The common difference \( d \) is calculated as:
\[ d = a_2 - a_1 = -5 - (-11) = 6. \]

Step 2: Write the general formula for an arithmetic sequence

The general formula for the \( n \)-th term of an arithmetic sequence is:
\[ a_n = a_1 + (n-1)d. \]

Step 3: Substitute the known values into the formula

Substitute \( a_1 = -11 \) and \( d = 6 \) into the formula:
\[ a_n = -11 + (n-1) \cdot 6. \]
Simplify the equation:
\[ a_n = 6(n-1) - 11. \]

Step 4: Compare with the given options

The equation \( a_n = 6(n-1) - 11 \) matches option B.

Final Answer

The correct answer is B.

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