Answer: The correct option is
(b) Square the number of the term, n.
Step-by-step explanation: We are given to examine the following sequence :
1, 4, 9, 16, 25, . . .
Also, we are to state the reason behind 36 being the next term in the sequence.
We see the following pattern in the terms of the given sequence :
[tex]a_1=1=1^2,\\\\a_2=4=2^2,\\\\a_3=9=3^2,\\\\a_4=16=4^2,\\\\a_5=25=5^2,\\\\\vdots~~~~\vdots~~~~\vdots[/tex]
Following the above pattern, we arrive at the n-th term of the sequence as follows :
[tex]a_n=n^2.[/tex]
Since we are to find the next, .i.e., the sixth term of the sequence, so
if n = 6, then
[tex]a_6=662=36.[/tex]
Thus, to get the n-th term, we square the number of the term.
The correct option is
(b) Square the number of the term, n.
