Question

Va rog cat mai corect

Answer 1

Răspuns:

Explicație pas cu pas:

an = a1 + (n - 1)*r

Sn = n*(a1 + an)/2

a1 = 4

a5 = a1 + 4r

16 = 4 + 4r

16 - 4 = 4r

12 = 4r

r = 12 : 4

r = 3

a10 = a1 + 9r = 4 + 9*3 = 31

S10 = 10*(4 + 31)/2 = 5*35 = 175

Answer 2

$\displaystyle 21.~~a_1=4,~a_5=16,~S_{10}=?\\\\ a_n=a_1+(n-1) \cdot r\\\\ a_5=16 \Rightarrow a_1+(5-1) \cdot r=16 \Rightarrow 4+4r=16 \Rightarrow 4r=16-4\Rightarrow 4r=12 \Rightarrow \\\\ \Rightarrow r=\frac{12}{4}\Rightarrow r=3\\\\ S_n=\frac{n[2a_1+(n-1)\cdot r]}{2} \\\\ S_{10}=\frac{10[2 \cdot 4+(10-1) \cdot 3]}{2} =\frac{10(8+9 \cdot 3)}{2} =\frac{10(8+27)}{2} =\frac{10 \cdot 35}{2} =\\\\ =\frac{350}{2} =175$