- Decreasing sequence
If the value of ‘d’ the common difference is negative, then the sequence is a decreasing
sequence.
Eg. : 10, 5, 0, –5, –10, ...- Sum of an AP
The sum of the ‘n’ terms of an A.P can be found using the formula,
Sn = n 2 [2a + (n-1) d]
where, Sn denotes the sum
n is the total number of terms
a is the first term
d is the common difference
If the last term of the sequence, denoted as ‘l’ is known, then the sum of the A.P is,Sn= 2 n []2a+(n-1)d = 2 n []a+{a + ()n− 1 d} = 2 n [a+l]
where ‘l’ is the last term of the sequence.Eg. :Consider the A.P. 2, 4, 6, 8, ... 24
Here the first term a=2
Common difference d = 4-2=2
Last term, l = 24(^) ∴ Number of terms,
=^242 −^2 +^1