Question

Find out the rule behind the formation of the sequence 1, 4.9, 16,..
a) Write next three terms.
b) what is the tenth term of this sequence?
c) is 900 a term of this sequence? if it is what is its position?
d) is 1000 a term of this sequence? why ? ​

Answer 1

(a) The next three terms of the given sequence are 25, 36 and 79.

(b) The tenth term of this sequence is 100.

(c) Yes, 900 will be a term of the given sequence.

(d) No, 1000 will not be a term of the given sequence.

Step-by-step explanation:

We are given the following sequence below;

1, 4, 9, 16,.........., and so on.

The given sequence follows the form;

$1^{2} = (1 \times 1) = 1$

$2^{2} = (2 \times 2) = 4$

$3^{2} = (3 \times 3) = 9$

$4^{2} = (4 \times 4) = 16$   and keeps ongoing...

This means that each number in our series is the perfect square of a particular number.

(a) The next three terms of the given sequence are;

$5^{2} = (5 \times 5) = 25$

$6^{2} = (6 \times 6) = 36$

$7^{2} = (7 \times 7) = 49$  

(b) The tenth term of this sequence will be;

$10^{2} =(10 \times 10)=100$

(c) Yes, 900 will be a term of the given sequence because it is a perfect square of the number 30, i.e. $30^{2} =900$.

The position of the term 900 will be at the 30th place in the sequence.

(d) No, 1000 will not be a term of the given sequence because there is no number whose perfect square is 1000.