Question

Examine the following sequence 1, 4, 9, 16, 25…. Why is 36 the next number in the sequence? Because the pattern is: a. Add the next even number c. Cube the number of the term, n b. Square the number of the term, n d. Add 2 + the number of the term, n Please select the best answer from the choices provided A

Answer 1

B. Square the number of the term, n

Answer 2

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 :

`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`

Following the above pattern, we arrive at the n-th term of the sequence as follows :

`a_n=n^2.`

Since we are to find the next, .i.e., the sixth term of the sequence, so

if n = 6, then

`a_6=662=36.`

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.