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In an arithmetic sequence, the first term, a_(1), is equal to 5 , and the sixth term, a_(6), is equal to 30 . 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 55 , and the sixth term, a6 a_{6} , is equal to 3030 . 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 55 , and the sixth term, a6 a_{6} , is equal to 3030 . 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 an arithmetic sequence, a1=5a_{1} = 5, and the sixth term, a6=30a_{6} = 30. We need to find the common difference, dd, of the sequence.
  2. Arithmetic sequence formula: The nnth term of an arithmetic sequence can be found using the formula an=a1+(n−1)da_n = a_1 + (n - 1)d, where a1a_1 is the first term and dd is the common difference.
  3. Express sixth term: We can use the formula to express the sixth term: a6=a1+(6−1)d=a1+5da_{6} = a_{1} + (6 - 1)d = a_{1} + 5d.
  4. Substitute values: Substitute the given values into the equation: 30=5+5d30 = 5 + 5d.
  5. Solve for d: Solve for d: 30=5+5d30 = 5 + 5d implies 30−5=5d30 - 5 = 5d, so 25=5d25 = 5d.
  6. Final common difference: Divide both sides by 55 to find dd: d=255d = \frac{25}{5}, which gives us d=5d = 5.

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