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Posted by **shabna** on Monday, February 27, 2012 at 3:55am.

- arithmetic -
**Bosnian**, Monday, February 27, 2012 at 9:22amAn arithmetic progression (A.P) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

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:

a n = a 1 + ( n - 1 ) d

a 1 = first term

In this case:

a 8 = a 1 + ( 8 - 1 ) d

a 8 = a 1 + 7 d = 18

a 15 = a 1 + ( 15 - 1 ) d

a 15 = a 1 + 14 d

a 9 = a 1 + ( 9 - 1 ) d

a 9 = a 1 + 8 d

a 15 - a 9 = ( a 1 + 14 d ) - ( a 1 + 8 d )

a 15 - a 9 = a 1 + 14 d - a 1 - 8 d

a 15 = a 1 - a1 + 14 d - 8 d

a 15 - a 9 = 6 d

a 15 - a 9 = 30

6 d = 30 Divide both sides by 6

d = 30 / 6

d = 5

a 8 = a 1 + 7 d = 18

a 1 + 7 * 5 = 18

a 1 + 35 = 18

a 1 = 18 - 35

a 1 = - 17

A.P

a n = - 17 + ( n - 1 ) * 5

- 17 , - 12 , - 7 , - 2 , 3 , 8 , 13 , 18 , 23 , 28 , 33 , 38 , 43 , 48 , 53

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