Question

Calculati suma : 1+3+5+.......13
Progresie aritmetica
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Answer 1

1 + 3 + 5 + ... + 13

aₙ = 13

a₁ = 1

a₂ = 3

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r = a₁ - a₂ = 3 - 1 = 2

aₙ = a₁ + ( n - 1 ) · r

⇒ 13 = 1 + ( n - 1 ) · 2

⇒ 12 = 2n - 2 ⇒ 14 = 2n ⇒ n = 7 ( progresia are 7 termeni )

S₇ = [( a₁ + a₇ ) / 2 ] · n = [( 1 + 13 ) / 2 ] · 7 = 7 · 7  = 49