[latex] -129,-6,-123,-11,...,-69,-56 [/latex] [latex] -129,-123,...,-69 [/latex] - ciąg [latex] (a_{n}) [/latex] [latex] -6,-11,...,-56 [/latex] - ciąg [latex] (b_{n}) [/latex] 1) Ciąg [latex] (a_{n}) [/latex] to ciąg arytmetyczny o różnicy [latex] r=3 [/latex]. [latex] a_{n}=a_{1}+(n-1)r [/latex] [latex] -69=-129+(n-1)*3 [/latex] [latex] -69=-129+3n-3 [/latex] [latex] 63=3n [/latex] [latex] n=21 [/latex] [latex] S_{n}=frac{a_{1}+a_{n}}{2}*n [/latex] [latex] S_{21}=frac{-129+(-69)}{2}*21=frac{-198}{2}*21=-99*21=-2079 [/latex] 2) Ciąg [latex] (b_{n}) [/latex] to ciąg arytmetyczny o różnicy [latex] r=-5 [/latex]. [latex] -56=-6+(n-1)*(-5) [/latex] [latex] -56=-6-5n+5 [/latex] [latex] -55=-5n [/latex] [latex] n=11 [/latex] [latex] S_{11}=frac{-6+(-56)}{2}*11=frac{-62}{2}*11=-31*11=-341 [/latex] Szukana suma to: [latex] S=-2079+(-341)=-2420 [/latex]
