Answer to Question #284928 in Algebra for Bjoy

Question

 Use the inductive reasoning to predict the next term in each list.

1. 4, 8, 12, 16, 20, 24, ?

2. 5, 11, 17, 23, 29, 35, ?

3. 1, 8, 27, 64, 125, ?

4. -2, 3, -4, 5, -6, 7, ?

5. 2, 5, 10, 17, 26, ?

Answer 1

1) $a_{n+1}=a_n+4.$

$a_7=a_6+4=24+4=28.$

2) $a_{n+1}=a_n+6.$

$a_7=a_6+6=35+6=41.$

3) $a_n=n^3.$

$a_6=6^3=216.$

4) $a_{n+2}=a_n-2.$

$a_7=a_5-2=-6-2=-8.$

5) $a_{n+1}=a_n+2n+1.$

$a_6=a_5+2*5+1=26+11=37.$