Question

Check if the series is an AP. Find the common difference $d$ and write three more terms of the the following series.

$2,4,8,16,....$

• A. Common difference: $2$ and Other three terms are: $32,64,128$
  
• B. Common difference: $4$ and Other three terms are: $24,32,40$
  
• C. Common difference: $8$ and Other three terms are: $20,24,28$
• D. None of these
  

Answer 1

Answer: (D)

None of these

Given series is $2,4,8,16,.....$

In an AP series, the difference between the consecutive terms remain same:

$a_2-a_1=4-2=2$

$a_3-a_2=8-4=4$

$a_3-a_2\ne a_2-a_1$

This shows that the difference of a term and the preceding terms is not always same. Hence, the given sequence is not an AP.