Question

Calcular a soma dos termos da P.A.( -16, -14, -12, ..., 84).

Answer 1

r → a2-a1 → -14-(-16) → -14+16 = 2

an=a1+(n-1)·r

84=-16+(n-1)·2

84=-16+2n-2

84=-18+2n

84+12=2n

96=2n

n=96/2

n=48

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Sn=(a1+an)·n/2

S48=(-16+8)·48/2

S48=(-8)·48/2

S48=-8·24

S48=-192

Answer 2

resolução!

r = a2 - a1

r = - 14 - (-16)

r = 2

an = a1 + ( n - 1 ) r

84 = - 16 + ( n - 1 ) 2

84 = - 16 + 2n - 2

84 = - 18 + 2n

84 + 18 = 2n

102 = 2n

n = 102 / 2

n = 51

Sn = ( a1 + an ) n / 2

Sn = ( - 16 + 84 ) 51 / 2

Sn = 68 * 51 / 2

Sn = 34 * 51

Sn = 1734