Question

Fie a0,a1,...,an,....termenii unei progresii aritmetice de ratie r. Stiind ca a50=26 si a100=51,sa se determine r si formula termenulii general an.

Answer 1

a₅₀= a₁ + 49r
a₁₀₀= a₁ + 99r

a₁ + 49r = 26
a₁ + 99r = 51
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a₁ + 49r - a₁ - 99r = 26-51
-50r = -25
r = 1/2.

26 = a₁ + 49/2
26 = (2a₁+49)/2
52 = 2a₁ + 49
a₁ = (52-49)/2
a₁ = 3/2
Formula termenului general:
a n = 3/2 + (n-1)*1/2 = ( 3 + n - 1)/2 = ( 2 + n)/2