In an arithmetic sequence, the first term, a1, is equal to 9 , and the sixth term, a6, is equal to 24 . 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 9 , and the sixth term, a6, is equal to 24 . Which number represents the common difference of the arithmetic sequence?d=2d=3d=4d=5
Given Terms: We are given the first term a1 and the sixth term a6 of an arithmetic sequence. The first term a1 is 9, and the sixth term a6 is 24. We need to find the common difference d.
Arithmetic Sequence Formula: The formula for the nth term of an arithmetic sequence is an=a1+(n−1)d, where a1 is the first term, d is the common difference, and n is the term number.
Express Sixth Term: We can use the formula to express the sixth term: a6=a1+(6−1)d=a1+5d.
Substitute Values: Substitute the given values into the equation: 24=9+5d.
Solve for d: Solve for d: 24=9+5d implies 24−9=5d, which simplifies to 15=5d.
Divide by 5: Divide both sides by 5 to find d: d=515.
Calculate d: Calculate the value of d: d=3.
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