# . Complete the following patterns

(i) 40, 35, 30 , , ,

(ii) 0, 2, 4 , , , .

(iii) 84, 77, 70 , , , .

(iv) 4.4, 5.5, 6.6 , , , .

(v) 1, 3, 6, 10 , , , .

(vi) 1, 1, 2, 3, 5, 8, 13, 21 , , , .

(This sequence is called FIBONACCI SEQUENCE)

(vii) 1, 8, 27, 64 , , , .

Explanation:

(i) The given series is 40, 35, 30 , , ,

The difference between the second and the first term is -5.

So, adding the difference, we get,

40,35,30,25,20,15.

(ii) The given series is 0, 2, 4 , , , .

The difference between the second and the first term is 2.

So, adding the difference, we get

0, 2, 4 ,6 ,8 , 10.

(iii) The given series is 84, 77, 70 , , , .

The difference between the second and the first term is -7.

So, adding the difference, we get

84, 77, 70 ,63 , 56, 49.

(iv) .The given series is 4.4, 5.5, 6.6 , , , .

The difference between the second and the first term is 1.1.

So, adding the difference, we get

4.4, 5.5, 6.6 ,7.7 , 8.8, 9.9.

(v) The given series is 1, 3, 6, 10 , , , .

The series increases by increasing difference.

1, 3, 6, 10 , , , .

So, =1,(1+2),(3+3),(6+4),(10+5),(15+6),(21+7)

1, 3, 6, 10 ,15 , 21,28 .

(vi) Fibonacci series is the series in which every term is the sum of its previous two terms.

So, the series will continue as

(1, 1, 2, 3, 5, 8, 13, 21 ,34 ,55 , 89)

(vii) The given series is

1, 8, 27, 64 , , , .

=13,23,33,43,53,63.

1, 8, 27, 64 ,125 , 216.

Completing the given patterns,

40,35,30,25,20,15.

0, 2, 4 ,6 ,8 , 10.

84, 77, 70 ,63 , 56, 49.

4.4, 5.5, 6.6 ,7.7 , 8.8, 9.9.

1, 3, 6, 10 ,15 , 21,28 .

(1, 1, 2, 3, 5, 8, 13, 21 ,34 ,55 , 89)

1, 8, 27, 64 ,125 , 216.