MATH SOLVE

4 months ago

Q:
# Make a conjecture about the next item in the sequence.1, 4, 16, 64, 256Select one:a. 1024b. 1025 c. 4096 d. 1022

Accepted Solution

A:

Answer:Option A is correct.Step-by-step 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 = 4First 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 = 1024Hence 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.