Question

Fie progresia aritmetica an de ratie r=-4 si cu a2+a5=3. Sa se determine a3

Answer 1

$r = - 4$

$a_{2} + a_{5} = 3$

$a_{3} = a_{2} + r = a_{2} - 4$

$a_{4} = a_{3} + r = a_{2} - 4 - 4 = a_{2} - 8$

$a_{5} = a_{4} + r = a_{2} - 8 - 4 = a_{2} - 12$

$a_{2} + a_{2} - 12 = 3$

$a_{2} + a_{2} = 3 + 12$

$2a_{2} = 15$

$a_{2} = \frac{15}{2}$

$a_{3} = a_{2} + r = \frac{15}{2} - 4 = \frac{7}{2}$