Question

dau coroana pentru raspunsurile corecte si intregi la ex 8,9

Answer 1

Răspuns:

Explicație pas cu pas:

8.

Cred ca este o greseala si ar fi trebuit sa fie

3 + 5 + 7 + .. + 21 = (3 +21) + (5 + 19) + (7 + 17) + (9 + 15) + (11 + 13)

= 24 + 24 + 24 + 24 + 24 = 24*5 = 120

9.

an = a1 + (n - 1)*r

a1 = 1

a4 = a1 + 3r

7 = 1 + 3r

6 = 3r

r = 2

a2018 = a1 + 2017r = 1 + 2017*2 = 1 + 4034 = 4035

Answer 2

$\displaystyle 8.~~3+5+7+...+21\\\\ n=(21-3):2+1=18:2+1=9+1=10\\\\ 3+5+7+...+21=\sum_{k=1}^{10}(2k+1)=2\sum_{k=1}^{10}k+\sum_{k=1}^{10}1=\\\\ =\not2 \cdot \frac{10(10+1)}{\not2} +10=10(10+1)+10=10 \cdot 11+10=110+10=120$

$\displaystyle 9.~~a_1=1,~a_4=7,~a_{2018}=?\\\\ a_n=a_1+(n-1) \cdot r\\\\ a_4=7\Rightarrow a_1+(4-1) \cdot r=7 \Rightarrow 1+3r=7 \Rightarrow 3r=7-1 \Rightarrow 3r=6\Rightarrow \\\\ \Rightarrow r=\frac{6}{3} \Rightarrow r=2\\\\ a_{2018}=1+2017 \cdot 2=1+4034=4035$