Question

Calculeaza cele 9 numere consecutive pare, avand in vedere ca suma lor este de 1620.

Answer 1

$(\text{x}+2\cdot1)+(\text{x}+2\cdot 2)+...+(\text{x}+2\cdot 9) = 1620 \\ \\ \text{x}+\text{x}+\underset{\text{de 9 ori}}{\underbrace{...}}+\text{x} +2\cdot1+2\cdot2+...+2\cdot 9 = 1620 \\ \\ 9\cdot\text{x}+2\cdot(1+2+3+...+9) = 1620\\ \\ 9\text{x}+2\cdot \dfrac{9\cdot(9+1)}{2} = 1620 \\ \\ 9\text{x}+9\cdot (9+1) = 1620 \\ \\ 9\text{x}+9\cdot 10 = 1620\\ \\ 9\cdot (\text{x}+10) = 1620 \\ \\ \text{x}+10 = \dfrac{1620}{9} \\ \\ \text{x}+10 = 180\\ \\ \text{x} = 180-10 \\ \\ \text{x} = 170$

$\Rightarrow Cele 9 numere consecutive pare sunt: \\ \\ (170+2), (170+4), (170+6),...,(170+18) \\ \\ \Leftrightarrow\\ \\ 172,174,176,178,180,182,184,186,188.$

Answer 2

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1 620 - 2×36=
1 620 - 72 =
1 548

1+1+1+1+1+1+1+1+1=9 (segmente egale)

1 548 : 9 = 172 (valoarea unui segment)

I nr. = 1×172=172

II nr. = 1×172+2=172+2=174

III nr. = 1×172+2×2=172+4=176

IV nr.=1×172+3×2=172+6=178

V nr.=1×172+4×2=172+8=180

VI nr.=1×172+5×2=172+10=182

VII nr.=1×172+6×2=172+12=184

VIII nr.=1×172+7×2=172+14=186

IX nr.=1×172+8×2=172+16=188

verificare:
172+174+176+178+180+182+184+186+188=1620