Question

Va rog ! dau coroana pentru raspuns intreg si corect!!

Answer 1

Răspuns:

56

Explicație pas cu pas:

$\boxed{a_{n} = a_{1} + (n - 1)\cdot r}$

$a_{5} = a_{3} + (5-3)r$

$11 = 5 + 2r$

$2r = 6 \implies r = 3$

$a_{1} = a_{3} - 2r = 5 - 6 = - 1$

$a_{7} = a_{1} + 6r = - 1 + 18 = 17$

$\boxed{ S_{n} = \dfrac{(a_{1} + a_{n})\cdot n}{2}}$

$S_{7} = \dfrac{(a_{1} + a_{7})\cdot 7}{2} = \dfrac{(- 1 + 17)\cdot 7}{2} = \bf 56$

Answer 2

$\displaystyle 28.~~a_3=5,~a_5=11,~S_7=?\\\\a_n=a_1+(n-1)\cdot r\\\\\left \{ {{a_3=5} \atop {a_5=11}} \right. \Rightarrow \left\{{{a_1+2r=5\Big|\cdot (-1)}\atop {a_1+4r=11}} \right. \Rightarrow \left \{ {{-a_1-2r=-5}\atop{a_1+4r=11}} \right.\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~----------\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/~~~~2r=6 \Rightarrow r=\frac{6}{2} \Rightarrow r=3\\\\a_1+2r=5\Rightarrow a_1+2 \cdot 3=5 \Rightarrow a_1+6=5 \Rightarrow a_1=5-6\Rightarrow a_1=-1$

$\displaystyle S_n=\frac{n[2a_1+(n-1) \cdot r]}{2} \\\\ S_7=\frac{7[2 \cdot(-1)+(7-1) \cdot 3]}{2} =\frac{7(-2+6 \cdot 3)}{2} =\frac{7(-2+18)}{2} =\frac{7 \cdot 16}{2} =\\\\=\frac{112}{2} =56$