Suma n-początkowych wyrazów ciągu geometrycznego
S_n=a_1*\frac{1-q^n}{1-q}
a)
a_1=2 , q=2
a_5=a_1*q^4=2*2^4=2*16=32
S_5=2*\frac{1-2^5}{1-2}=\frac{2(1-32)}{-1}=-2*(-31)=62
b)
a_2=2 , q=-2
a_1*q=a_2
a_1=\frac{a_2}{q}=\frac{2}{-2}=-1
a_5=a_2*q^3=2*(-2)^3=2*(-8)=-16
S_5=-1*\frac{1-(-2)^5}{1-(-2)}=\frac{-1[1-(-32)]}{1+2}=\frac{-33}{3}=-11
c)
a_3=2 , q=\frac{1}{2}
a_1*q^2=a_3
a_1=\frac{a_3}{q^2}=\frac{2}{(\frac{1}{2})^2}=\frac{2}{\frac{1}{4}}=2*4=8
a_5=a_3*q^2=2*(\frac{1}{2})^2=2*\frac{1}{4}=\frac{1}{2}
S_5=8*\frac{1-(\frac{1}{2})^5}{1-\frac{1}{2}}=\frac{8(1-\frac{1}{32})}{\frac{1}{2}}=16(1-\frac{1}{32})=16-\frac{1}{2}=15\frac{1}{2}