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In an arithmetic sequence, the first term, 
a_(1), is equal to 8 , and the fifth term, 
a_(5), is equal to 20 . Which number represents the common difference of the arithmetic sequence?

d=2

d=3

d=4

d=5

In an arithmetic sequence, the first term, a1 a_{1} , is equal to 88 , and the fifth term, a5 a_{5} , is equal to 2020 . Which number represents the common difference of the arithmetic sequence?\newlined=2 d=2 \newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5

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Q. In an arithmetic sequence, the first term, a1 a_{1} , is equal to 88 , and the fifth term, a5 a_{5} , is equal to 2020 . Which number represents the common difference of the arithmetic sequence?\newlined=2 d=2 \newlined=3 d=3 \newlined=4 d=4 \newlined=5 d=5
  1. Identify Given Terms: Identify the given terms in the arithmetic sequence.\newlineWe are given the first term a1a_{1} and the fifth term a5a_{5} of an arithmetic sequence.\newlinea1=8a_{1} = 8\newlinea5=20a_{5} = 20
  2. Use nth Term Formula: Use the formula for the nnth term of an arithmetic sequence to express a5a_{5}. The nnth term of an arithmetic sequence is given by an=a1+(n1)da_{n} = a_{1} + (n - 1)d, where dd is the common difference. For the fifth term, n=5n = 5, so we have: a5=a1+(51)da_{5} = a_{1} + (5 - 1)d
  3. Substitute Known Values: Substitute the known values into the equation for a5a_{5}. We know that a1=8a_{1} = 8 and a5=20a_{5} = 20, so we substitute these values into the equation: 20=8+(51)d20 = 8 + (5 - 1)d
  4. Simplify Equation: Simplify the equation to solve for dd.20=8+4d20 = 8 + 4dSubtract 88 from both sides:208=4d20 - 8 = 4d12=4d12 = 4dDivide both sides by 44:d=3d = 3

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