Oblicz : 1+9+17+....+x=175 daje naaj :)

a1=1 r=8 n=? Sn=(a1+an)*n/2=[a1+a1+(n-1)r]n/2 podstawiam [2+8(n-1)]*n=350 2n+8n²-8n=350 8n²-6n-350=0 4n²-3n-175=0 Δ=9+16*175=2809 √Δ=53 n=(3+53)/8=56/8=7  n2∉D x=a7 x=a1+6r=1+6*8=49 ODP  x=49 Pozdr Hans

Suma ciagu arytmetycznego: [latex]\a_1=1, r=9-1=8, S_n=175 \ \x=a_n \ \S_n=frac{2*a_1+r(n-1)}{2}*n \ \frac{2+8(n-1)}{2}*n=175 \ \(1+4n-4)*n=175 \ \4n^2-3n-175=0 \ \4n^2-28n+25n-175=0 \ \4n(n-7)+25(n-7)=0 \ \(n-7)(4n+25)=0[/latex] [latex]\n-7=0 vee 4n+25=0 \ \n=7 vee n=-frac{25}{4} otin N_+ \ \x=a_7=1+8*6=1+48=49 \ \Odp. x=49[/latex]