Question

prog aritmetica (an)n>sau egal1
a3=5 si a5=1 S7

Answer 1

$\left \{ {a_3 = 5} \atop {a_3 = a_1 + 2 r }} \right. =\ \textgreater \ a_1+2r = 5 \\ \left \{ {a_5 = 1} \atop {a_5 = a_1 + 4 r }} \right. =\ \textgreater \ a_1+4r = 1$
     Faci sistem din cele doua ecuatii si o sa obtii:
$\left \{ {{a_1+2r = 5} \atop {a_1+4r = 1}} \right.$
     Le scazi si o sa obtii:
 $-2r = 4 =\ \textgreater \ r = -2 =\ \textgreater \ a_1 = 5-2r=5-2\cdot(-2)= 5+4=9$
$S_7 = \frac{(a_1+a_7)\cdot7}{2}$
$a_7 = a_1 + 6r = 9+6\cdot(-2)= 9-12 =-3$
$S_7 = \frac{(a_1+a_7)\cdot7}{2}= \frac{(9-3)\cdot7}{2} = \frac{6\cdot7}{2} = \frac{42}{2} = 21$