In an arithmetic sequence, the first term, a1, is equal to 5 , and the sixth term, a6, is equal to 15 . Which number represents the common difference of the arithmetic sequence?d=2d=3d=4d=5
Q. In an arithmetic sequence, the first term, a1, is equal to 5 , and the sixth term, a6, is equal to 15 . Which number represents the common difference of the arithmetic sequence?d=2d=3d=4d=5
Given terms: We are given the first term of an arithmetic sequence, a1=5, and the sixth term, a6=15. We need to find the common difference, d, of the sequence.
Arithmetic sequence formula: The nth term of an arithmetic sequence can be found using the formula an=a1+(n−1)d, where a1 is the first term and d is the common difference.
Expressing sixth term: We can use the formula to express the sixth term: a6=a1+5d. We know that a6=15 and a1=5, so we can substitute these values into the equation to find d.
Substituting values: Substituting the known values gives us 15=5+5d. We can now solve for d.
Solving for d: Subtracting 5 from both sides of the equation gives us 10=5d.
Final common difference: Dividing both sides of the equation by 5 gives us d=2.
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