what is formula to find the sum of n terms of AP
Answers
Answer:The formula says that the sum of the first n terms of our arithmetic sequence is equal to n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.
Sum of arithmetic progression
The sum of arithmetic progression is denoted by Sn. It is nothing but the sum of 'n terms of an A.P. with first term 'a' and common difference 'd'.
The formula for sum of n terms of A.P. is
Sn=
n
2
[2a+(n−1)d]
Sn=
n
2
[a+l] , where l = last term = a + (n -1 )d
Proof : Let a1,a2,a3,...,an be an A.P. with first term as 'a' and common difference as 'd'.
a1 = a; a2 = a + d; a3 = a + 2d ; ... an = a + (n -1)d
Sn=a1+a2+a3+...+an−1+an
⇒ Sn = a + (a + d) + (a + 2d) + … + [ a + (n-2)d] + [ a + (n -1 )d] -----(i)
Write the above equation in reverse order we get,
Sn = [ a + (n -1 )d] + [ a + (n-2)d] + … + (a + 2d) + (a + d) + a ----- (ii)
Now add the two equations,
2Sn = [ 2a + (n -1 )d] + [ 2a + (n-1)d] + …+ [2a + (n-1)d]
[2a + (n-1)d] repeats ‘n’ times
∴ 2Sn = n [ 2a + (n -1 )d]
Sn=
n
2
[ 2a + (n -1 )d]
Since the last term l = a + (n – 1)d
∴ Sn=
n
2
[ a + a + (n -1 )d]
Sn=
n
2
[a + l ]
Note : In the above formula there are 4 unknown quantities. So if any three are given then we can find the forth one.
In the sum of Sn of n terms of a sequence is given then the nth term an of the sequence can determined by using the following formula .
Hallo dear ,
formula to find the sum of n terms of AP
Sn = n/2 [ 2a+( n-1 ) d ] .
Where ,
n = number of terms .
a = first term.
d = common difference.
Sn = sum of all the terms.
Thank you .
#@mark it brainlist answer.