Question

Sa se gaseasca primul termen si ratia unei progresii aritmetice ,daca:
c5=27 , c27=60

Answer 1

$\displaystyle c_5=27,~c_{27}=60\\c_5=27 \Rightarrow c_{5-1}+r=27 \Rightarrow c_4+r=27 \Rightarrow c_1+4r=27 \Rightarrow c_1=27-4r \\ c_{27}=60 \Rightarrow c_{27-1}+r=60 \Rightarrow c_{26}+r=60 \Rightarrow c_1+26r=60 \Rightarrow \\ \Rightarrow 27-4r+26r=60 \Rightarrow -4r+26r=60-27 \Rightarrow 22r=33 \Rightarrow \\ \Rightarrow r= \frac{33}{22} \Rightarrow \boxed{r= \frac{3}{2} }$
$\displaystyle c_1=27-4r \Rightarrow c_1=27-4 \cdot \frac{3}{2} \Rightarrow c_1=27- \frac{12}{2}\Rightarrow c_1=27-6\Rightarrow \\ \Rightarrow \boxed{c_1=21}$