$a, 2a, 3a, 4a, \dots$ are $APs$? If they form an $AP,$ find the common difference $d$ and write three more terms.

(A) The given sequence is $a, 2a, 3a, 4a, \dots$
To check if it is an $AP,$ we calculate the difference between consecutive terms:
$a_2 - a_1 = 2a - a = a$
$a_3 - a_2 = 3a - 2a = a$
$a_4 - a_3 = 4a - 3a = a$
Since the difference $a_{k+1} - a_k$ is constant $(d = a)$,the sequence forms an $AP.$
The next three terms are:
$a_5 = 4a + a = 5a$
$a_6 = 5a + a = 6a$
$a_7 = 6a + a = 7a$