Question

va rog mult , dau coroana , ex 15

Answer 1

Răspuns:

Explicație pas cu pas:

a)

x = 6 + 12 + 18 + ....+ 288

a1 = 6; an = 288; r = 6

an = a1 + (n - 1)r

288 = 6 + (n - 1)*6 = 6 + 6n - 6 = 6n

n = 288 : 6 = 48

Sn = n(a1 + an)/2 = 48(6 + 288)/2 = 48*294/2 = 7056 = 84^2

√x = 84

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b)

x = 4 + 8 + 12 + .... + 196

196 = 4 + (n - 1)*4 = 4 + 4n - 4 = 4n

n = 196 : 4 = 49

x = 49(4 + 196)/2 = 49*200/2 = 49*100 = (7*10)^2 = 70^2

√x = 70

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c)

x = 1 + 3 + 5 + ....+ 1001

1001 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1

2n = 1002

n = 1002 : 2 = 501

x = 501(1 + 1001)/2 = 501*1002/2 = 501*501 = 501^2

√x = 501

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d)

x = 1 + 3 + 5 + ...+ 2021

2021 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1

2n = 2021 + 1 = 2022

n = 2022 : 2 = 1011

x = 1011 (1 + 2021)/2 = 1011*2022/2 = 1011*1011 = 1011^2

√x = 1011

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e)

x = 1203 + 2 + 4 + 6 + .... + 2404

2404 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n

n = 2404 : 2 = 1202

x = 1203 + 1202*(2 + 2404)/2 = 1203 + 1202*2406/2 = 1203 + 1202*1203 =

= 1203(1 + 1202) = 1203*1203 = 1203^2

√x = 1203