Question

Va rog cat mai corect si intreg dau coroana pentru cel mai corect raspuns!
Pentru ambele!

Answer 1

Explicație pas cu pas:

40.

$\begin{cases} b_{2} + b_{1} = 8 \\ b_{2} - b_{1} = 4\end{cases}$

$2b_{2} = 12 \implies b_{2} = 6$

$b_{1} = 8 - 6 \implies b_{1} = 2$

$q = \dfrac {b_{2}}{b_{1}} = \dfrac {6}{2} = 3$

$S_{3} = \dfrac{b_{1}\cdot ({q}^{3} - 1) }{q - 1} = \dfrac{2\cdot ({3}^{3} - 1) }{3 - 1} = \dfrac{2\cdot 26}{2} = 26$

sau:

$b_{3} = q \cdot b_{2} = 3 \cdot 6 = 18$

$S_{3} = b_{1} + b_{2} + b_{3} = 2 + 6 + 18 = 26$

41.

$(b_{3})^{2} = 6 \cdot 24 = 144 = 12^{2} \implies b_{3} = 12$

$q = \dfrac {b_{3}}{b_{2}} = \dfrac {12}{6} = 2$

$b_{1} = \dfrac {b_{2}}{q} = \dfrac {6}{2} = 3$

$S_{9} = \dfrac{b_{1}\cdot ({q}^{9} - 1) }{q - 1} = \dfrac{3\cdot ({2}^{9} - 1) }{2 - 1} = \\ = \dfrac{3\cdot (512 - 1) }{1} = 3\cdot 511 = 1533$