Question

Make a conjecture about the next item in the sequence.

1, 4, 16, 64, 256
Select one:

a. 1024

b. 1025

c. 4096

d. 1022

Answer 1

A

Step-by-step explanation: you times each one by 4

Answer 2

Option A is correct.

Explanation:

Given terms,

1 , 4 , 16 , 64 , 256.

If we observe the equation, we can easily say that the terms are getting multiplied by 4 to get the next one.

Since this equation has a common ratio, this can be solved by using the properties of geometric progressions.

From the properties of geometric progressions :

• nth term = a r^( n - 1 ) , where a is the first term, r is the common ratio between the terms and n is the number of terms.

Here,

Common Ratio ( or r ) = any term( except first ) / previous terms = 64 / 16 = 16 / 4 = 4

First terms = 1

Therefore,

= > Next term should be : 1 x ( 4 )^( 6 - 1 ) { Since next term will be 6th term }

= > Next term = 1 x 4^5

= > Next term = 1024

Hence the required next term is 1024.

Option A is correct.

Or

Here we can see that the terms are written in the form of 4^n where n is any whole number.

Since 246 is 4^4 , and terms are increasing in order of 1, next term should be 4^5 i.e. 1024 .

Thus, option A is correct.