Determine AP

Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71

Result

d =  19

Solution:

a3=7 a4+a5=71 a3+d+a3+2d=71 2a3+3d=71 d=(71−2⋅ a3)/3=(71−2⋅ 7)/3=19a_{ 3 } = 7 \ \\ a_{ 4 }+a_{ 5 } = 71 \ \\ a_{ 3 }+d+a_{ 3 }+2d = 71 \ \\ 2a_{ 3 } + 3d = 71 \ \\ d = (71-2 \cdot \ a_{ 3 })/3 = (71-2 \cdot \ 7)/3 = 19

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