Question

W pewnym ciagu geometrycznym a6=5 i a8=10. Jakie moga byc wyrazy a1, a 7 i a10 tego ciagu?

Answer 1

Ze względu że jest to ciąg geometryczny czyli

a7/a6 = a8/a7 <=> a7^2 = a6*a8

a7= 50 ^(1/2) = 5 *[(2)^(1/2)]


q= a7/a6 = 2^(1/2)

aN= a1 * [q^(n-1)]

a6 =a1 * ( 2^(1/2)) ^5 = a1 * 4* [ 2^(1/2)]

a1 = a6 /{4* [ 2^(1/2)]} = 5/ {4* [ 2^(1/2)]} ={ 5/8 } * ( 2^(1/2))


a10= a1 * (q^9) = { 5/8 } * ( 2^(1/2)) * [[2^(9/2)] = 20


Czyli

a1 = { 5/8 } * ( 2^(1/2))

a7= 5 *[(2)^(1/2)]

a10 =20