Question

Se considera progresia aritmetica (Xn)n € N cu al 4 lea termen egal cu 16, iar diferenta dintre al 10 lea si al 12 lea termen egala cu 4 . Calculati X2013.

Answer 1

$\displaystyle x_{12}-x_{10}=4\Rightarrow x_1+11r-x_1-9r=4\Rightarrow r=2\\\displaystyle x_4=16\Rightarrow x_1+3r=16\Rightarrow x_1=10\\\displaystyle x_{2013}=x_1+2012r=10+2012\cdot2=4034$