Write an Equation using the following arithmetic sequence: 5, _____, ______, 32

1 answer
Question:

Write an Equation using the following arithmetic sequence: 5, _____, ______, 32

Answers

Answer:The sequence is:5, 14, 23, 32Step-by-step explanation:We know that an Arithmetic sequence with a₁ and the commo difference 'd' has the nth term such as:aₙ = a₁ + (n-1)dGiven the arithmetic sequence5, _____, ______, 32here:a₁ = 5n = 4aₙso substituting a₁ = 5, n = 4 and aₙ = 32 in the nth termaₙ = a₁ + (n-1)d32 = 5 + (4-1)d32 = 5 + 3d3d = 32-53d = 27divide both sides by 33d/3 = 27/3d = 9Therefore, the common difference: d = 9Determining the 2nd term:Using the formulaaₙ = a₁ + (n-1)dsubstitute n = 2, a₁ = 5, d = 9a₂ = 5 + (2-1)9a₂ = 5 + 1(9)a₂ = 5 + 9a₂ = 14Determining the 3rd term:Using the formulaaₙ = a₁ + (n-1)dsubstitute n = 3, a₁ = 5, d = 9a₃ = 5 + (3-1)9a₃ = 5 + 2(9)a₃ = 5 + 18a₃ = 23Thus, the sequence becomes:5, 14, 23, 32

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