Fifth member

Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.

Result

a5 =  47

Solution:

a2+a5=73 d=7 a1+d+a1+4d=73 a1=(73−5⋅ d)/2=(73−5⋅ 7)/2=19 a5=a1+4⋅ d=19+4⋅ 7=47a_{2}+a_{5}=73 \ \\ d=7 \ \\ a_{1}+d+a_{1}+4d=73 \ \\ a_{1}=(73-5 \cdot \ d)/2=(73-5 \cdot \ 7)/2=19 \ \\ a_{5}=a_{1}+4 \cdot \ d=19+4 \cdot \ 7=47

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