# Math

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

• Math -

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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