Wyznacz wzór ogólny ciągu arytmetycznego (an): a) a4= -9    a15= -3 b) a5= 4    a21= 8

[latex]a_n=a_1+(n-1)r \a) a_4=a_1+(4-1)r=a_1+3r=-9 \a_1_5=a_1+(15-1)r=a_1+14r=-3 \ \ left { {{a_1+3r=-9} atop {a_1+14r=-3}} ight. - \-11r=-6 \r= frac{6}{11} \a_1=-9-3r=-9- frac{18}{11} =- frac{117}{11} \a_n=-frac{117}{11} +(n-1)* frac{6}{11} \ \b)a_5=a_1+(5-1)r=a_1+4r=4 \a_2_1=a_1+(21-1)r=a_1+20r=8 \ \ left { {{a_1+4r=4} atop {a_1+20r=8}} ight. - \-16r=-4 \r= frac{1}{4} \a_1=4-4r=4-1=3 \a_n=3+(n-1)* frac{1}{4} [/latex]

a) a₄ = - 9 a₁₅ = - 3 ----------------- a₄ = a₁ +3r = - 9 / * - 1 a₁₅ = a₁ + 14r = - 3 - a₁ - 3r = 9 a₁ + 14r = - 3 dodajemy stronami - a₁ - 3r + a₁ + 14r = 9 - 3 11r = 6 r = 6/11 -------------------- a₁ + 3 * r = - 9 a₁ = - 9 - 3 * 6/11 = - 9 - 18/11 = - 10i 7/11 ------------------------------------ an = a₁ + (n - 1)r = - 10i7/11 + (n - 1) * 6/11 = - 10 i 7/11 + 6/11 n - 6/11 = 6/11 n - 11 i 2/11 b) a₅ = 4 a₂₁ = 8 -------------- a₁ + 4r = 4/* - 1 a₁ + 20r = 8 - a₁ - 4r = - 4 a₁ + 20r = 8 - a₁ - 4r + a₁ + 20r = - 4 + 8 16r = 4 r = 4/16 = 1/4 --------------------- a₁ + 4r = 4 a₁ + 4 * 1/4 = 4 a₁ + 1 = 4 a₁ = 4 - 1 = 3 ------------------- an = a₁ + (n - 1)r = 3 + (n - 1)* 1/4 = 3 + 1/4n - 1/4 = 1/4n + 2 i 3/4