There are 6 terms in an A.P. 6th term is 3 times the second term and 4th term is 4 times the first term. if the 5th term is 15 find the terms

Answer 1

2nd term = a+d
6th term = a + 5d
"the 6th term is 3 times the second term" -->
a+5d = 3(a+d)
a+5d = 3a + 3d
2d = 2a
a = d

"the 5th term is 15" --->
a+4d = 15
but a = d
5d = 15
d = 3
then a = 3

"the 4th term is 4 times the first term" -->
a+3d = 4a
3d = 4a
d= a
this last piece of information was not needed, but confirms our answer

the terms are
3 6 9 12 15 and 18