Posted by Jatin on Thursday, January 5, 2012 at 12:12am.
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:
an = a1 + ( n - 1 ) * d
a3 = a1 + ( 3 - 1 ) * d
a3 = a1 + 2 d
a3 = 4 a1
4 a1 = a1 + 2 d
4 a1 - a1 = 2d
3 a1 = 2 d Divide both sides with 2
3 a1 / 2 = d
d = 3 a1 / 2
an = a1 + ( n - 1 ) * d
a6 = a1 + ( 6 - 1 ) * d = 17
17 = a1 + 5 d
17 = a1 + 5 * 3 a1 / 2
17 = a1 + 15 a1 / 2
17 = 2 a1 / 2 + 15 a1 / 2
17 = 17 a1 / 2 Multiply both sides with 2
34 = 17 a1 Divide both sides with 17
34 / 17 = a1
2 = a1
a1 = 2
d = 3 a1 / 2
d = 3 * 2 / 2
d = 6 / 2
d = 3
a1 = 2 , d = 3
A.P.
2 , 5 , 8 , 11 , 14 , 17 , 20 , 23 ...
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