In an arithmetic sequence, the first term, a1, is equal to 7 , and the fifth term, a5, is equal to 31 . Which number represents the common difference of the arithmetic sequence?d=3d=4d=5d=6
Q. In an arithmetic sequence, the first term, a1, is equal to 7 , and the fifth term, a5, is equal to 31 . Which number represents the common difference of the arithmetic sequence?d=3d=4d=5d=6
Identify Given Terms: Identify the given terms in the arithmetic sequence.The first term is a1=7, and the fifth term is a5=31.
Recall Formula: Recall the formula for the nth term of an arithmetic sequence.The nth term is given by an=a1+(n−1)d, where d is the common difference.
Set Up Equation: Set up the equation for the fifth term using the formula. a5=a1+(5−1)dSubstitute the given values.31=7+(5−1)d
Simplify Equation: Simplify the equation to find the common difference d.31=7+4d31−7=4d24=4d
Divide to Solve: Divide both sides of the equation by 4 to solve for d.d=424d=6
More problems from Find a value using two-variable equations: word problems