Question

Calculati suma primilor 40 termeni ai progresiei aritmetice (an)n>1 stiind ca a5=25 si a22=93​

Answer 1

$\it a_{22}=a_5+(22-5)r \Rightarrow 93=25+17r\bigg|_{-25} \Rightarrow 68=17r\bigg|_{:17} \Rightarrow r=4\\ \\ \\ a_1=a_5-4r =a_1=25-4\cdot4 =9\\ \\ a_{40}=a_1+39r=9+39\cdot4=9+156=165\\ \\ S_{40}=\dfrac{(a_1+a_{40})\cdot40}{2}=\dfrac{(9+165)\cdot40}{2}=174\cdot20$