Question

Qual a soma dos termos da PG (10,5,...5/16)?

Answer 1

resolução!

q = a2 / a1

q = 5 / 10

q = 1/2

an = a1 * q^n - 1

5/16 = 10 * (1/2)^n - 1

5/16 ÷ 10 = (1/2)^n - 1

5/16 * 1/10 = (1/2)^n - 1

5/160 = (1/2)^n - 1

1/32 = (1/2)^n - 1

(1/2)^5 = (1/2)^n - 1

n - 1 = 5

n = 5 + 1

n = 6

Sn = a1 ( q^n - 1 ) / q - 1

Sn = 10 ( 1 - (1/2)^6 - 1 ) / 1 - 1/2

Sn = 10 ( 1 - 1/64 ) / 1/2

Sn = 10 ( 63/64 ) / 1/2

Sn = 10 * 63/64 * 2/1

Sn = 1260/64

Sn = 315/16