CBSEi Class 10 Sequences (AP and GP) CORE

(vi) Area of fourth square =
Similarly, area of fifth square = and area of 6 th square = and so on.
Area of the nth square = , where n is a natural number.
(vii) Next number in the pattern =
Similarly, next to this number = and so on.
Clearly, the nth number = where n is a natural number.
(viii) Observing the pattern, the next number = 9 x 48 [Next number of 1, 3, 5, 7 is 9
(Why?) and that of 3 , 6, 12, 24 is 48 (Why?)]
(ix) Here, we see that
1 st number = 1
2 nd number = 1
3 rd number = 1+1=2
4 th number = 1+2=3
5 th number = 2+3=5
6 th number = 3+5=8
7 th number = 5+8=13
8 th number = 8+13=21
9 th number = 13+21=34
10 th number = 21+34 = 55 and so on.
Here, every number, except the first two numbers, is the sum of preceding
two numbers.
This pattern is known as Fibonacci Sequence, named after a great Italian
mathematician Leonardo Fibonacci (1170-1250).
(x) Here, 1 st number =
39