Question

C |+2|+|+51 +|+81 +...+|+29|= d |-2|¹+|-2|²+...+|-2|20 = C | +2 | + | +51 + | +81 + ... + | +29 | = d | -2 | ¹ + | -2 | ² + ... + | -2 | 20 =​

Answer 1

Explicație pas cu pas:

c) progresie aritmetică

$a_{1} = 2, r = 3, n = 10$

$S_{n} = \frac{(a_{1} + a_{n}) \cdot n}{2}$

$| + 2| + | + 5| + | + 8| + ... + | + 29| =$

$= 2 + 5 + 8 + ... + 29$

$= 2 + (2 + 1 \cdot 3) + (2 + 2 \cdot 3) + ... + (2 + 9\cdot 3)$

$= \frac{(2 + 29) \cdot 10}{2} = \frac{31\cdot 10}{2} = 155$

d) progresie geometrică

$b_{1} = 2, q = 2, n = 20$

$S_{n} = \frac{b_{1} \cdot ({q}^{n} - 1)}{q - 1}$

${ | - 2| }^{1} + { | - 2| }^{2} + { | - 2| }^{3} + ... + { | - 2| }^{20} =$

$= {2}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{20}$

$= \frac{2 \cdot ( {2}^{20} - 1)}{2 - 1}$

$= 2 \cdot ( {2}^{20} - 1)$