Question

Se considera progresia aritmetica ( an ) n ≥ 1 in care r = 7/2 si a9 = 29. Sa se calculeze S15.

Answer 1

$\displaystyle a_9=29,~r= \frac{7}{2} ,~S_{15}=? \\ \\ a_9=29 \Rightarrow a_{9-1}+r=29 \Rightarrow a_8+r=29 \Rightarrow a_1+8r=29 \Rightarrow \\ \\ \Rightarrow a_1+8 \cdot \frac{7}{2} =29 \Rightarrow a_1+ \frac{56}{2} =29 \Rightarrow a_1+28=29 \Rightarrow \\ \\ \Rightarrow a_1=29-28 \Rightarrow a_1=1 \\ \\ S_{15}= \frac{2 \cdot 1+(15-1) \cdot \frac{7}{2} }{2} \cdot 15 \\ \\ S_{15}= \frac{2+14 \cdot \frac{7}{2} }{2} \cdot 15$

$\displaystyle S_{15}= \frac{2+ \frac{98}{2} }{2} \cdot 15 \\ \\ S_{15}= \frac{2+49}{2} \cdot 15 \\ \\ S_{15}= \frac{51}{2} \cdot 15 \\ \\ S_{15}= \frac{765}{2}$