Question

Calculati suma a 25 de numere naturale consecutive stiind ca primul si al patrulea numar sunt direct proportionale cu numerele 4 si 5.

Answer 1

$\mathtt{a_1+a_2+a_3+...+a_{25}=x}$

$\mathtt{a+(a+1)+(a+2)+...+(a+24)=x}$

$\mathtt{\frac{a}{4}=\frac{a+3}{5}=k}$

$\mathtt{a=4k}$

$\mathtt{a+3=5k=\textgreater a=5k-3}$

$\mathtt{4k=5k-3}$

$\mathtt{k=3}$

$\mathtt{a=4\cdot3=12}$

$\mathtt{x=12+13+14+...+36}$

$\mathtt{x=36+35+34+...+12}$

$\mathtt{2x=48+48+48+...+48}$
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                          25 de termeni

$\mathtt{2x=25\cdot48}$

$\mathtt{x=\frac{25\cdot48}{2}=600}$