A) 25
B) 26
C) 27
D) 28
Correct Answer: B
Solution :
Let the three consecutive natural numbers are n, n + 1 and n + 2. According to question, \[{{n}^{2}}+{{(n+1)}^{2}}+{{(n+2)}^{2}}=2030\] \[\Rightarrow \] \[{{n}^{2}}+{{n}^{2}}+2n+1+{{n}^{2}}+4n+4=2030\] \[\Rightarrow \] \[3{{n}^{2}}+2n-675=0\] \[\Rightarrow \] \[{{n}^{2}}+2n-675=0\] \[\Rightarrow \] \[(n+27)(n-25)=0\] \[\Rightarrow \] \[n=25\] \[(\because n\ne -27)\] \[\therefore \] Middle number \[=n+1=25+1=26\]
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