Question

Se considera progresia aritmetica in care a1=3 si a3=7. Sa se calculeze suma primilor 10 termeni ai progresiei.

Answer 1

a1=3
a3=7
a3=a1+2r -->2r=a3-a1-->2r=7-3-->2r=4 |:2-->r=2
an=a1+(n-1) *r  -->3+9*2 =21
an=21
S=(a1+an) *n supra 2-->S=(3+21)*10  supra 2=24 *5 =120
S10=120

Answer 2

$\displaystyle a_1=3 , ~a_3=7,~S_{10}=? \\ a_3=7 \Rightarrow a_{3-1}+r=7 \Rightarrow a_{2}+r=7 \Rightarrow a_1+2r=7 \Rightarrow \\ \Rightarrow 3+2r=7 \Rightarrow 2r=7-3 \Rightarrow 2r=4 \Rightarrow r= \frac{4}{2} \Rightarrow r=2 \\ \boxed{S_n= \frac{2a_1+(n-1) \cdot r}{2}\cdot n } \\ \\ S_{10}= \frac{2 \cdot 3+(10-1) \cdot 2}{\not2} \cdot \not10 \\ S_{10}=(6+9 \cdot 2) \cdot 5 \\ S_{10}=(6+18) \cdot 5 \\ S_{10}=24 \cdot 5 \\ S_{10}=120$