Progresie aritmetica

[Al3x]

\( a_2+a_{40}=16 \)
\( a_5=28 \)
\( a_1=?,\ r=? \)

[Alin]

\( \ a_2+\ a_{40}=16 \) adica \( \ 2a_1+40r=16 => \ a_1+20r=8 (1) \). Din \( \ a_5=28 \) scoatem \( \ a_1+4r=28 (2) \). Din \( (1), (2) => 16r=-20 => r=-\frac {20}{16}=-\frac {5}{4} \). Stim ratia si \( \ a_5=28 \) si aflam ca \( \ a_1=33 \).