Question

Wyznacz roznice r ciagu arytmetycznego, majac dane :
a) Sn=518, a1= 50, n=14
b)Sn= 728, n=16, an=63 Potrzebne na już :)

Answer 1

a)

Sn = 518, a1 = 50 , n = 14

 

więc

a14 = a1 + 13 r = 50 + 13 r

S14 =  0,5 *( a1 + a14)*14 = 518

7*( 50 + 50 + 13 r) = 518  / : 7

100 + 13 r = 74

13 r = 74 - 100 = - 26  / : 13

r = - 2

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b)

Sn = 728,  n = 16, an = 63

 

więc

a16 = a1 + 15 r = 63 = >  a1 = 63 - 15 r

oraz

S16 = 0,5 *( a1 + a16)*16 = 8*( 63 - 15 r + 63) = 8*( 126 - 15 r) = 728  / : 8

126 - 15 r = 91

15 r = 126 - 91 = 35 / : 15

r = 7/3

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