Posted by Anonymous on Thursday, March 1, 2012 at 11:43pm.
An 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 5 = 30
a 1 + ( 5 - 1 ) d = 30
a 1 + 4 d = 30
a 1 = 30 - 4 d
a 12 = 65
a 1 + ( 12 - 1 ) d = 65
a 1 + 11 d = 65
30 - 4 d + 11 d = 65
30 + 7 d = 65
7 d = 65 - 30
7 d = 35 Divide both sides by 7
d = 35 / 7
d = 5
a 1 = 30 - 4 d
a 1 = 30 - 4 * 5
a 1 = 30 - 20
a 1 = 10
The sum S of the first n values of a finite sequence is given by the formula:
S n = ( n / 2 ) * [ 2 a 1 + ( n - 1 ) d ]
In tis case :
a 1 = 10
d = 5
n = 20
S 20 = ( 20 / 2 ) * [ 2 * 10 + ( 20 - 1 ) 5 ]
S 20 = 10 * ( 20 + 19 * 5 )
S 20 = 10 * ( 20 + 95 )
S 20 = 10 * 115
S 20 = 1150