Question

1. Efectuati :
1+4+7+.....+91=
nr. termeni=​

Answer 1

Răspuns:

Explicație pas cu pas:

1+4+7+.....+91 =

rația = 3 (4-1; 7-4;....)

(91-1) : 3 + 1 = 90 : 3 + 1 = 30 + 1 = 31 termeni are suma

= 31 × (1+91) : 2 =

= 31 × 92 : 2 =

= 2852 : 2 =

= 1426

Answer 2

Avem suma termenilor unei progresii aritmetice cu rația 3.

$\it a_n=a_1+(n-1)r=1+(n-1)\cdot3=1+3n-3=3n-2=91|_{+2} \Rightarrow \\ \\ \Rightarrow 3n=93|_{:3} \Rightarrow n=31\ (num\breve arul\ termenilor\ sumei)\\ \\ \\ S_{31}=\dfrac{(a_1+a_{31})\cdot 31}{2}=\dfrac{(1+91)\cdot31}{2}=\dfrac{92\cdot31}{2}=46\cdot31=1426$