Răspuns
Explicație pas cu pas:
3) a)
a → primul nr.
a + 2 → al doilea nr. par consecutiv
a + 4 → al treilea nr. par consecutiv
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a + 18 → al X-lea nr. par consecutiv
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10 × a + ( 2 + 4 + 6 + 8 + ..... + 18 ) = 90
10 × a + 2 × ( 1 + 2 + 3 + ...... + 9 ) = 90
10 × a + 2 × 9 × 10 : 2 = 90
10 × a + 90 = 90
10 × a = 90 - 90
a = 0 → primul nr.
0 + 2 + 4 + 6 + 8 + 10 + .....+ 18 = 90 → suma celor 10 numere naturale pare consecutive
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b)
10 × a + ( 2 + 4 + 6 + ..... + 18 ) = 100
10 × a + 2 × ( 1 + 2 + 3 + .... + 9 ) = 100
10 × a = 2 × 9 × 10 : 2 = 100
10 × a = 100 - 90
a = 10 : 10
a = 1 → primul numar impar
1 + 3 + 5 + ......+ 19 = 10 × 20 / 2 = 100 → suma celor 10 numere impare consecutive
→ ( 19 - 1 ) : 2 + 1 = 10 termeni are suma
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c)
7 × a + ( 2 + 4 + 6 + 8 + 10 + 12 ) = 98
7 × a + 2 × ( 1 + 2 + 3 + ....... + 6 ) = 98
7 × a + 2 × 6 × 7 : 2 = 98
7 × a + 42 = 98
7 × a = 98 - 42
a = 56 : 7
a = 8 → primul numar par
S = 8 + 10 + 12 + 14 + 16 + 18 + 20 → suma celor 7 numere pare consecutive
S = 98
