Question

Арифмитическая прогрессия​

Answer 1

Объяснение:

a6= a1+5d

-2= -12+5d

10=5d

d=2

a17= a1+16d= -12+16*2= 20

Answer 2

Дано:

$\displaystyle \tt (a_n)$ - арифметическая прогрессия

$\displaystyle \tt a_1=-12$

$\displaystyle \tt a_6=-2$

Найти:

$\displaystyle \tt a_{17} \: - \: ?$

1) Находим разность $\displaystyle \tt d$:

$\displaystyle \tt a_n=a_1+d(n-1) \: \to \: a_6=a_1+5d\\\displaystyle \tt -2=-12+5d\\\displaystyle \tt 5d-12=-2\\\displaystyle \tt 5d=-2+12\\\displaystyle \tt 5d=10\\\displaystyle \tt d=\frac{10}{5}\\\displaystyle \tt \textbf{d\:=\:2}$

2) Находим $\displaystyle \tt a_{17}$:

$\displaystyle \tt a_n=a_1+d(n-1) \: \to \: a_{17}=a_1+16d\\\displaystyle \tt a_{17}=-12+16\cdot2\\\displaystyle \tt a_{17}=-12+32\\\displaystyle \tt \boxed{\bold{a_{17}=20}}$

$\displaystyle \tt a_{17}=20$