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The first term of an AP is 13 and the last term is 57.If the arithmetic progression consists of 40 terms, calculate the sum of all the terms. 

Solution

A₁ = 13, n=40, A_n = 57

S_n = n(A₁ + A_n)

       2

S₂₀ = 40(13 + 57)

         2

S₂₀ = 20 x 70

S₂₀ = 1400

Hence the sum of all 20 terms is 1400.

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The first term of an AP is 11 and the last term is 163.If the arithmetic progression consists of 60 terms, calculate the sum of all the terms.