Question

Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference. $3,6,12,24,......$

Answer 1

Given sequence is,

$3,6,12,24,...\dots$

first term of this A.P is $a_1=3$

second term of this A.P is $a_2=6$

third term of this A.P is $a_3=12$

the condition for an sequence to be an A.P is their must be a common difference $(i.e.,d=a_{n+1}-a_n)$

putting $n=1$ in above equation

$d=a_2-a_1=6-3=3$

putting n=2 in above equation

$d=a_3-a_2=12-6=6$

as we can see we get two values of $d$,

but in an $A.P$ their must be a single value of $d$ which means for this sequence we can't define a common difference.

hence this sequence not form an $A.P$