Answer:
(a) 2,5,8,11,14, 17
(b) 1000,200,40,8,1.6
(c) 1,4,9,16,25,36
(d) 1,1,2,3,5,8, 12, 17
Step-by-step explanation:
The given sequences are
(a) 2,5,8,11,__,__
Here, 5 -2 = 3 , 8 - 5 =3
So, each term is 3 MORE than the previous term
So, next two terms are 11 + 3 = 14 and 14 + 3 = 17
Hence, the pattern is 2,5,8,11,14, 17
(b) 1000,200,40,__,__
Here, [tex]\frac{1000}{200} = 5, \frac{200}{40} = 5[/tex]
So, each term is (1/5) times the previous term
So, next two terms are [tex]\frac{40}{5} = 8, \frac{8}{5} = 1.6[/tex]
Hence, the pattern is 1000,200,40,8,1.6
(c) 1,4,9,16,__,__
Here, 4 -1 = 3 , 9 - 4 =5, and 16 - 9 = 7
So, the difference in the series is 3, 5 , 7,...
So, next two terms are 16 + 9 = 25 and 25 + 11 = 36
Hence, the pattern is 1,4,9,16,25,36
(d) 1,1,2,3,5,8,__,_
Here, 1-1 = 0, 2-1 = 1, 3-2 = 1, 5-3 = 2, 8-5 = 3
So, the series with difference is 0, 1 , 1 , 2 , 3
so, the next terms are 8 + 4 = 12, and 12 + 5 = 17
Hence, the pattern is 1,1,2,3,5,8, 12, 17
