In an A.P.the third term is 4 times the first term and the 6th term is 17. Find the series
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 ...