In an arithmetic sequence, the first term, a1, is equal to 8 , and the fifth term, a5, is equal to 20 . 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 8 , and the fifth term, a5, is equal to 20 . Which number represents the common difference of the arithmetic sequence?d=2d=3d=4d=5
Identify Given Terms: Identify the given terms in the arithmetic sequence.We are given the first term a1 and the fifth term a5 of an arithmetic sequence.a1=8a5=20
Use nth Term Formula: Use the formula for the nth term of an arithmetic sequence to express a5. The nth term of an arithmetic sequence is given by an=a1+(n−1)d, where d is the common difference. For the fifth term, n=5, so we have: a5=a1+(5−1)d
Substitute Known Values: Substitute the known values into the equation for a5. We know that a1=8 and a5=20, so we substitute these values into the equation: 20=8+(5−1)d
Simplify Equation: Simplify the equation to solve for d.20=8+4dSubtract 8 from both sides:20−8=4d12=4dDivide both sides by 4:d=3
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