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In an arithmetic sequence, the first term, a_(1), is equal to 3 , and the fourth term, a_(4), is equal to 24 . Which number represents the common difference of the arithmetic sequence? d=4 d=5 d=6 d=7

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 33 , and the fourth term, a4 a_{4} , is equal to 2424 . Which number represents the common difference of the arithmetic sequence?\newlined=4 d=4 \newlined=5 d=5 \newlined=6 d=6 \newlined=7 d=7

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Q. In an arithmetic sequence, the first term, a1 a_{1} , is equal to 33 , and the fourth term, a4 a_{4} , is equal to 2424 . Which number represents the common difference of the arithmetic sequence?\newlined=4 d=4 \newlined=5 d=5 \newlined=6 d=6 \newlined=7 d=7
  1. Given terms: We are given the first term of the arithmetic sequence a1a_{1} is 33 and the fourth term a4a_{4} is 2424. The common difference dd can be found by using the formula for the nth term of an arithmetic sequence, which is an=a1+(n−1)da_{n} = a_{1} + (n - 1)d. We can set up the equation for the fourth term.
  2. Set up equation: Substitute the known values into the formula to find the common difference. We have a4=24a_{4} = 24, a1=3a_{1} = 3, and n=4n = 4. So, 24=3+(4−1)d24 = 3 + (4 - 1)d.
  3. Simplify equation: Simplify the equation: 24=3+3d24 = 3 + 3d. Subtract 33 from both sides to isolate the term with dd: 24−3=3d24 - 3 = 3d.
  4. Isolate term: Perform the subtraction: 21=3d21 = 3d. Now, divide both sides by 33 to solve for dd: 21÷3=d21 \div 3 = d.
  5. Calculate common difference: Calculate the division: 7=d7 = d. So, the common difference of the arithmetic sequence is 77.

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