Question

w ciągu arytmetycznym dane:

a₃=6 :a₄=8

a₁=7 : a₁₀=28

oblicz a₂₀ i s₂₀

prosze o pomoc

Answer 1

r = a4 - a3 = 8 - 6 = 2

a3 = 6

a1 + 2r = 6

a1 = 6 - 2 * 2

a1 = 2

 

a20 = a1 + 19r = 2 + 19 * 2 = 2 + 38 = 40

S20 = (a1 + a20) * n / 2 = (2 + 40) * 20 / 2 = 420

 

a1 = 7

a10 = 28

a1 + 9r = 28

7 + 9r = 28

9r = 28 - 7

9r = 21

r = 21/9 = 7/3 = 2 i 1/3

 

a20 = a1 + 19r = 7 + 19 * 7/3= 7 + 133/3 = (21 + 133)/3 = 154/3 = 51 i 1/3

S20 = (7 + 51 i 1/3) * 20 / 2 = 58 i 1/3 * 10 = 583 i 1/3

 

Answer 2

a)   a 1+2r=6   .................(1)

a 1+3r=8...................(2) 

od rownania (2) odejmujemy (1)

r=2

liczymy a 1

a 1+4=6

a 1=2

a 20=a 1+19r

a 20=2+19·2

a 20=40

================

Sn=n(a 1+a n)/2

 S 20=20(2+40)/2

S20=420

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b) a 1=7

a 10=28

a 10=a 1+9r

7+9r=28

9r=28-7

9r=21    /:9

r=21/9

r=7/3

============ 

a 20=a 1+19r

a 20=7+19·7/3

a 20=7+133/3

a 20=51 1/3

==================

S 20=20(7+51 1/3)/2

S 20=10·58 1/3

S 20=583 1/3

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