zad 1 a₁ = 8 r = 5 a₅ = ? S₁₇ - S₅ = ? ------------------------------------- ogólny wzór ciągu arytmetycznego an = a₁ + (n - 1)r ogólny wzór na sumę ciągu arytmetycznego Sn = (a₁ + an)n/2 ----------------------------------------- a₅ = a₁ + 4r = 8 + 4 * 5 = 8 + 20 = 28 a₁₇ = a₁ + 16r = 8 + 16 * 5 = 8 + 80 = 88 S₅ = (8 + 28)5/2 = 36 * 5/2 = 180/2 = 90 S17 = (8 + 88)17/2 = 96 * 17/2 = 1632/2 = 816 S₁₇ - S₅ = 816 - 90 = 726 zad 2 A log₂2 + log₂6 - log₂3 = log₂2*6/2 = log₂6 B (log₈5 + log₈6) : (log₈60 - log₈2) = log₈5 * 6/(60 :2) = log₈30/30 = log₈1 C 2log₂4 + log₂2 - log₂4 = log₂4² + log₂2/4 = log₂16 + log₂1/2 = log₂16 * 1/2 = log₂8
a5=8+4*5=28 a n=a1+(n-1)*r a17=8+16*5=88 S5=8+282 *5=90 S17=8+882 *17=816 S17-S5=816-90=726 2a) log2 2+log2 6-log2 3=log2(2*6)-log2 3= =log2 12 -log2 3= =log2(122)= =log2 4 log2 4=x 2^x=4 2^x=2² x=2 b) (log8 5+log8 6)÷(log8 60-log8 2)= =log8(3030)= log8 1=0 c) 2log2 4+log2 2-log2 4= =log2 16+log2 2-log2 4= =log2(16*20-log2 4= log2 32 -log2 4= log2(322)= log2 8 log2 8=x 2^x=8 2^x=2³ x=3
1.w ciągu arytmetycznym (an) wyraz a1=8 i różnica r=5. oblicz sumę wyrazów od 5 do 17 włącznie 2.oblicz: A) log₂2+log₂6-log₂3= B) (log₈5+log₈6) : (log₈60-log₈2)= C) 2log₂4+log₂2-log₂4=...
