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In an arithmetic sequence, the first term, 
a_(1), is equal to 7 , and the fifth term, 
a_(5), is equal to 31 . Which number represents the common difference of the arithmetic sequence?

d=3

d=4

d=5

d=6

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 77 , and the fifth term, a5 a_{5} , is equal to 3131 . Which number represents the common difference of the arithmetic sequence?\newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5 \newlined=6 d=6

Full solution

Q. In an arithmetic sequence, the first term, a1 a_{1} , is equal to 77 , and the fifth term, a5 a_{5} , is equal to 3131 . Which number represents the common difference of the arithmetic sequence?\newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5 \newlined=6 d=6
  1. Identify Given Terms: Identify the given terms in the arithmetic sequence.\newlineThe first term is a1=7a_{1} = 7, and the fifth term is a5=31a_{5} = 31.
  2. Recall Formula: Recall the formula for the nnth term of an arithmetic sequence.\newlineThe nnth term is given by an=a1+(n1)da_{n} = a_{1} + (n - 1)d, where dd is the common difference.
  3. Set Up Equation: Set up the equation for the fifth term using the formula. \newlinea5=a1+(51)da_{5} = a_{1} + (5 - 1)d\newlineSubstitute the given values.\newline31=7+(51)d31 = 7 + (5 - 1)d
  4. Simplify Equation: Simplify the equation to find the common difference dd.31=7+4d31 = 7 + 4d317=4d31 - 7 = 4d24=4d24 = 4d
  5. Divide to Solve: Divide both sides of the equation by 44 to solve for dd.\newlined=244d = \frac{24}{4}\newlined=6d = 6

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