ARITHMETIC PROGRESSION 1

The first term of an AP is 13 and the last term is 57.If the arithmetic progression consists of 20 terms, calculate the sum of all the terms. 

Solution

A₁ = 5, n=20, A_n = 57

S_n = n(A₁ + A_n)

    2

S₂₀ = 20(13 + 57)

      2

S₂₀ = 10 x 70

S₂₀ = 700

Hence the sum of all 20 terms is 700.

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The first term of an AP is 17 and the last term is 83.If the arithmetic progression consists of 40 terms, calculate the sum of all the terms.