Question

B1=3, b2=-24
b5,S5=?

Answer 1

[tex]\it \dfrac{..}{..} \ \ b_1 = 3,\ \ \ b_2 = -24 \\\;\\ b_5 = ?\ \ \ S_5 = ?[/tex]

[tex]\it b_2=b_1\cdot q \Rightarrow q=\dfrac{b_2}{b_1}=\dfrac{-24}{3}=-8 \\\;\\ b_5 = b_1\cdot q^4 = 3\cdot(-8)^4 = 12 288 \\\;\\ S_5 = 3\cdot\dfrac{(-8)^5-1}{-8-1} = 3\cdot\dfrac{(-8)^5-1}{-9} = \dfrac{8^5+1}{3} = 10 923[/tex]