Question

Помогите решить пж!!!!!

Answer 1

1.

$a_{1} = 70 \: \: \: d = - 3$

$a_{18} = a_{1} + 17d = 70 + 17( - 3) = 70 - 51 = 19$

2.

-21;-18;-15..

d= -18 - (-21)=3

$s = \frac{a_{1} + a_{20} }{2} \times 20 = \frac{ - 21 + ( - 21 +19 d)}{2} \times 20 = \frac{ - 21 + ( - 21 + 19 \times 3)}{2} \times 20 = \frac{ - 21 + ( - 21 + 57)}{2} \times 20 = (- 21 + 36) \times 10 = 150$

3.

$b_{n} = 4n - 2$

$b _{1} = 4 \times 1 - 2 = 2$

$b_{40} = 4 \times 40 - 2 = 158$

$s = \frac{b_{1} + b_{40} }{2} \times 40 = \frac{2 + 158}{2} \times 40 = 160 \times 20 = 3200$

4.

$a_{1} = 11.6 \: \: \: \: \: a_{15} = 17.2$

$a_{15} = a_{1} + 14d = 17.2 \\ 11.6 + 14d = 17.2 \\ 14d = 17.2 - 11.6 = 5.6 \\ d = 0.4$

$30.4 = a_{1} + xd \\ 11.6 + 0.4x = 30.4 \\ 0.4x = 30.4 - 11.6 = 18.8 \\ x = 47$

значит,что 30,4 является 48м членом прогрессии