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In an arithmetic sequence, the first term, , is equal to , and the fourth term, , is equal to . Which number represents the common difference of the arithmetic sequence?
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Q. In an arithmetic sequence, the first term, , is equal to , and the fourth term, , is equal to . Which number represents the common difference of the arithmetic sequence?
- Given terms: We are given the first term of the arithmetic sequence, , and the fourth term, . To find the common difference, , we can use the formula for the nth term of an arithmetic sequence, which is .
- Set up equation: We can set up the equation for the fourth term using the formula: .
- Substitute values: Substitute the given values into the equation: $\(39\) = \(9\) + (\(4\) - \(1\))d.
- Simplify equation: Simplify the equation: \(39 = 9 + 3d\).
- Isolate term with \(d\): Subtract \(9\) from both sides to isolate the term with \(d\): \(39 - 9 = 3d\).
- Perform subtraction: Perform the subtraction: \(30 = 3d\).
- Divide to solve for d: Divide both sides by \(3\) to solve for d: \(d = \frac{30}{3}\).
- Final result: Perform the division: \(d = 10\).
