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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 15 . Which number represents the common difference of the arithmetic sequence?

d=2

d=3

d=4

d=5

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 55 , and the sixth term, a6 a_{6} , is equal to 1515 . Which number represents the common difference of the arithmetic sequence?\newlined=2 d=2 \newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5

Full solution

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 1515 . Which number represents the common difference of the arithmetic sequence?\newlined=2 d=2 \newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5
  1. Given terms: We are given the first term of an arithmetic sequence, a1=5a_1 = 5, and the sixth term, a6=15a_6 = 15. 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+(n1)da_n = a_1 + (n - 1)d, where a1a_1 is the first term and dd is the common difference.
  3. Expressing sixth term: We can use the formula to express the sixth term: a6=a1+5da_{6} = a_{1} + 5d. We know that a6=15a_{6} = 15 and a1=5a_{1} = 5, so we can substitute these values into the equation to find dd.
  4. Substituting values: Substituting the known values gives us 15=5+5d15 = 5 + 5d. We can now solve for dd.
  5. Solving for dd: Subtracting 55 from both sides of the equation gives us 10=5d10 = 5d.
  6. Final common difference: Dividing both sides of the equation by 55 gives us d=2d = 2.

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