Question

найдите закономерность,по которой составлена последовательность и дополните ее следующими двумя числами:
1) 5 6 8 11 15 20 ....
2) 2 3 5 8 13 21 ....
3) 45 44 42 39 35 ....
4)1 4 9 16 25 36 49 ....
5)1 8 27 64 125 216 ....
6) 2 9 28 65 126 217 ....

Answer 1

$\tt 1) \ 5 \overset{+1}{\Longrightarrow}6\overset{+2}{\Longrightarrow}8\overset{+3}{\Longrightarrow}11\overset{+4}{\Longrightarrow}15\overset{+5}{\Longrightarrow}20\overset{+6}{\Longrightarrow}26\overset{+7}{\Longrightarrow}33... \\\\ 2) \ 2 \overset{+1}{\Longrightarrow}3\overset{+2}{\Longrightarrow}5\overset{+3}{\Longrightarrow}8\overset{+5}{\Longrightarrow}13\overset{+8}{\Longrightarrow}21\overset{+13}{\Longrightarrow}34\overset{+21}{\Longrightarrow}55...$

$\tt 3) \ 45 \overset{-1}{\Longrightarrow}44\overset{-2}{\Longrightarrow}42\overset{-3}{\Longrightarrow}39\overset{-4}{\Longrightarrow}35\overset{-5}{\Longrightarrow}30\overset{-6}{\Longrightarrow}24\overset{-7}{\Longrightarrow}17...\\\\ 4) \ 1 \overset{+3}{\Longrightarrow}4\overset{+5}{\Longrightarrow}9\overset{+7}{\Longrightarrow}16\overset{+9}{\Longrightarrow}25\overset{+11}{\Longrightarrow}36\overset{+13}{\Longrightarrow}49\overset{+15}{\Longrightarrow}64\overset{+17}{\Longrightarrow}81...$

$\tt 5) \ \overset{1^3}{\Longrightarrow}1 \overset{2^3}{\Longrightarrow}8\overset{3^3}{\Longrightarrow}27\overset{4^3}{\Longrightarrow}64\overset{5^3}{\Longrightarrow}125\overset{6^3}{\Longrightarrow}216\overset{7^3}{\Longrightarrow}343\overset{8^3}{\Longrightarrow}512...$

$\tt 6) \ \overset{1^3+1}{\Longrightarrow}2 \overset{2^3+1}{\Longrightarrow}9\overset{3^3+1}{\Longrightarrow}28\overset{4^3+1}{\Longrightarrow}65\overset{5^3+1}{\Longrightarrow}126\overset{6^3+1}{\Longrightarrow}217\overset{7^3+1}{\Longrightarrow}344\overset{8^3+1}{\Longrightarrow}513...$