Question

Fie sirul:13,18,23....
a) aflati termenul 50 apoi calculati suma primilor 50 termeni
b) 2018 ce loc ocupa apoi calculati suma s=13+18+....2018

Answer 1

13, 18,  23 .........

( n - 13 ) : 5 + 1 = 50

( n - 13 ) : 5 = 50 - 1

n - 13 = 49 × 5

n = 245 + 13

n = 258 → al 50 -lea termen al sirului

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sau:  

a₁ = 13

a₂ = 13 + 5 = 18

a₃ = 13 + 2 x 5 = 23

a₄ = 13 + 3 x 5 = 28

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a₅₀ = 13 + 49 x 5 = 13 + 245 = 258 → al 50 lea termen al sirului

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S = 13 + 18 + 23 + ....... + 258

S = 50 × ( 13 + 258 ) / 2

S = 25 × 271

S = 6 775

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b)  S = 13 + 18 + ....... + 2018

a₁ = 13

a₂ = 13 + 1 x 5 = 18

a₃ = 13 + 2 x 5 = 23

a₄ = 13 + 3 x 5 = 28

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13 +  ( n - 1 ) x 5 = 2 018

n - 1 = ( 2018 - 13 ) : 5

n - 1 = 2005 : 5

n = 401 + 1

n = 402

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a₄₀₂ = 13 + 401 x 5 = 13 + 2005 = 2 018