Question

Find the common difference of an AP: $1^2,5^2,7^2,73,....$

Answer 1

Given sequence is,

$1^2,5^2,7^2,73,...\dots$

first term of this A.P is $a_1=1^2=1$

second term of this A.P is $a_2=5^2=25$

third term of this A.P is $a_3=7^2=49$

fourth term of this A.P is $a_4=73$

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

$d=a_2-a_1=25-1=24$

putting n=2 in above equation

$d=a_3-a_2=49-25=24$

putting n=3 in above equation

$d=a_4-a_3=73-49=24$as we can see we get a common difference $d=24$ for this sequence hence this sequence forms an A.P with first term $a_1=1$ and common difference $d=24$