Question

in an AP sum of an n term is 2n^2+3n find common difference

Answer 1

Let here "n" suffix be "x"
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Given: Sₓ = 2x² + 3x

aₓ = Sₓ - Sₓ₋₁
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Sₓ-₁ = 2(x-1)² + 3(x-1)

        = 2(x²-2x+1) + 3(x-1)

        = 2x² - 4x + 2 + 3x - 3

        = 2x² - x - 1
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Then, aₓ = 2x² + 3x - 2x² + x + 1

               = 4x + 1
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As aₓ = 4x + 1

Then, a₁ = 4(1) + 1
               
            a = 4 + 1 = 5

           a₂ = 4(2) + 1

                = 8 + 1 = 9

Then d = a₂ - a₁    

         d = 9 - 5 = 4

Hence common difference (d) is 4 
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