Question

se da a7+a11=54 si a5+a12=51 Sa se afle a1=? , r=? ,a12=?, a33=?.Suma primilor 5 termeni .​

Answer 1

Răspuns:

a₁ = 3 ; r = 3

a₁₂ = 36

a₃₃ = 99

S₅ = 45

Explicație pas cu pas:

{a₇+a₁₁=54

{a₅+a₁₂=51 <=>

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{a₁+6r+a₁+10r = 54

{a₁+4r+a₁+11r = 51

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{2a₁+16r = 54

{2a₁+15r = 51

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=> r = 3 ; 2a₁+15·3 = 51 =>

a₁ = (51-45):2 => a₁ = 3

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a₁₂ = 3+11·3 = 36

a₃₃ = 3+32·3 = 99

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S₅ = a₁+a₂+...+a₅ = a₁+a₁+r+a₁+2r+a₁+3r+a₁+4r = 5a₁+10r = 5·3+10·3 = 45

S₅ = 45