Question

Oblicz sume 8 wyrazow ciagu geonetrycznego, w ktorym a2=3, a6=243

Answer 1

A2=3 a2=aq
a6=243 a6=aq^5

3=aq => 3/q=a
243=aq^5

243= 3/q * q^5

243= 3q^4
81=q^4
q=3

a= 3/3
a=1

S8= a * (1- q^8)/(1-q)
S8= 1 * (1- 3^8)(1-3)
S8= (1-6561)/(-2)
S8= 3280

Answer 2

A2 = 3
a6 = 243
a2 = a1*q
a6 = a1*q^5
-----------------
a6 : a2 = a1*q^5 : a1*q = q^4
a6 : a2 = 243 : 3 = 81
q^4 = 81
q = 3
a2 = a1*q ---> a1 = a2 : q = 3 : 3 = 1
a1 = 1
a8 = a1*q^7 = 1*3^7 = 2187
S8 = [1 - q^8]/[ 1-q] = [1-6561]/[1-3] = (-6560)/(-2) = 3280

Answer 3

Oblicz sume 8 wyrazow ciagu geonetrycznego, w ktorym a2=3, a6=243

a6/ a2=g⁴=243/3
g⁴=81
g=3
a1=1
S8=1*(1-3⁸)/(1-3)
S8=(1-3⁸)/(-2)
S8=(1-6561)/(-2)
S8=(-6560)/(-2)
S8=3280