Question

Give the next two terms in each of these patterns

(a) 2,5,8,11,__,__
(b) 1000,200,40,__,__
(c) 1,4,9,16,__,__
(d) 1,1,2,3,5,8,__,__

Answer 1

(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

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,
`(1000)/(200)  = 5, (200)/(40)  = 5`

So, each term is (1/5) times the previous term

So, next two terms are
`(40)/(5)  = 8, (8)/(5)  = 1.6`

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