Question

oblicz sume n kolejnych wyrazów ciągu geometrycznego, jeśli a1=-2, q=1/2 (0,5), n=3

-- zadanie bardzo pilne

Answer 1

a1 = - 2

q = 1/2

n = 3

zatem

S3 = a1*[ 1 - q^3]/( 1 - q)

S3 = -2*[ 1 - (1/2)^3] /( 1 - 1/2) = - 2*[ 1 - 1/8] /(1/2)

S3 = -2* (7/8)*2 = - 4*(7/8) = - 7/2 = - 3,5

Odp. S3 = - 3,5

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Sn = a1*[ 1 - q^n]/[1 - q]

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Answer 2

Sn = a1 * (1 -q^n) / (1 - q)   --- wzór na sumę Sn w ciagu geometrycznym

n = 3

a1 = -2

q = 1/2

podstawiamy do wzoru i otrzymujemy

S3 = (-2) * (1 - (1/2)^3) / (1 - 1/2)

S3 = (-2) * (1 - 1/8) / (1/2)

S3 = (-2) * (7/8 : 1/2)

S3 = (-2) * (7/8 * 2/1)

S3 = (-2) * 7/4

S3 = -7/2

S3 = -3,5