The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1:5, find the A.P.
S7 = 
[2a + (7 – 1) d]
182 = 
[2a + 6d]
52 = 2a + 6d
a + 3d = 26 (i)
Acc. To question,
a17 = 5a4
a + 16d = 5(a + 3d)
d = 4a
d = 4(26 – 3d) [from (i)]
13d = 104
d = 8
Putting the value of d in (i), we get
a = 26 – 3*8) = 2
a1 = a = 2
a2 =a + d = 2 + 8 = 10
a3 = a + 2d = 2 + 2(8) = 18
Hence, The A.P. is 2, 10, 18,…
54