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
