Sum of the seventeen numbers

The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.

Result

s =  34

Solution:

a1=1 d=1 n=17 a17=a1+d⋅ (n−1)=1+1⋅ (17−1)=17 s17=a1+a172⋅ n=1+172⋅ 17=153  s1=1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+18=154   s=16+18=34a_{1}=1 \ \\ d=1 \ \\ n=17 \ \\ a_{17}=a_{1} + d \cdot \ (n-1)=1 + 1 \cdot \ (17-1)=17 \ \\ s_{17}=\dfrac{ a_{1}+a_{17} }{ 2 } \cdot \ n=\dfrac{ 1+17 }{ 2 } \cdot \ 17=153 \ \\ \ \\ s_{1}=1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+18=154 \ \\ \ \\ \ \\ s=16+18=34

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