Question

URGENT VA ROG
calculati ratia primului termen al progresiei aritmetice care a10= 13 si a20= 155

Answer 1

a=(10+13):2=23:2=12 r1
a=
(20+155):2=157:2=78r5 (aicia e mai complicat)

12+78+1+1=92

Answer 2

$\displaystyle a_{10}=13,~a_{20}=155 \\ \\ a_{10}=13 \Rightarrow a_{10-1}+r=13 \Rightarrow a_9+r=13 \Rightarrow a_1+9r=13 \Rightarrow \\ \\ \Rightarrow a_1=13-9r \\ \\ a_{20}=155 \Rightarrow a_{20-1}+r=155 \Rightarrow a_{19}+r=155 \Rightarrow a_1+19r=155 \Rightarrow \\ \\ \Rightarrow 13-9r+19r=155 \Rightarrow -9r+19r=155-13 \Rightarrow 10r=142 \Rightarrow \\ \\ \Rightarrow r= \frac{142}{10} \Rightarrow \boxed{r= \frac{71}{5} }$

$\displaystyle a_1=13-9r \Rightarrow a_1=13-9 \cdot \frac{71}{5} \Rightarrow a_1=13- \frac{639}{5} \Rightarrow \\ \\ \Rightarrow 5a_1=65-639 \Rightarrow 5a_1=-574 \Rightarrow \boxed{a_1=- \frac{574}{5} }$