Question

if third term of A.P. is four times the first term and sixth term is 7,find the progression.

Answer 1

(a+2d )=4a.
2d=3a
a = 2d/3 ------------(1)

; a+5d =7
a = 7-5d -----------(2)
equating equation (1) & (2), we get
2d/3 = 7-5d
2d = 21- 15d
21 = 17d
d = 21/17
put value of d in equation (1)
a = 2×21/17×3
= 42/51 = 14/17

required A.P is
14/17 , 63/17, 84/17, 105/17 , .......................

hope it helped,
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Answer 2

Solution is attached below in image