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In an arithmetic sequence, the first term, a_(1), is equal to 9 , and the fourth term, a_(4), is equal to 39 . Which number represents the common difference of the arithmetic sequence? d=9 d=10 d=11 d=12

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 99 , and the fourth term, a4 a_{4} , is equal to 3939 . Which number represents the common difference of the arithmetic sequence?\newlined=9 d=9 \newlined=10 d=10 \newlined=11 d=11 \newlined=12 d=12

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Q. In an arithmetic sequence, the first term, a1 a_{1} , is equal to 99 , and the fourth term, a4 a_{4} , is equal to 3939 . Which number represents the common difference of the arithmetic sequence?\newlined=9 d=9 \newlined=10 d=10 \newlined=11 d=11 \newlined=12 d=12
  1. Given terms: We are given the first term of the arithmetic sequence, a1=9a_{1} = 9, and the fourth term, a4=39a_{4} = 39. To find the common difference, dd, we can use the formula for the nth term of an arithmetic sequence, which is an=a1+(n−1)da_{n} = a_{1} + (n - 1)d.
  2. Set up equation: We can set up the equation for the fourth term using the formula: a4=a1+(4−1)da_{4} = a_{1} + (4 - 1)d.
  3. Substitute values: Substitute the given values into the equation: $\(39\) = \(9\) + (\(4\) - \(1\))d.
  4. Simplify equation: Simplify the equation: \(39 = 9 + 3d\).
  5. Isolate term with \(d\): Subtract \(9\) from both sides to isolate the term with \(d\): \(39 - 9 = 3d\).
  6. Perform subtraction: Perform the subtraction: \(30 = 3d\).
  7. Divide to solve for d: Divide both sides by \(3\) to solve for d: \(d = \frac{30}{3}\).
  8. Final result: Perform the division: \(d = 10\).

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