if the nth term of an AP is (2n+1) find the sum of first n terms of the AP - Maths - Arithmetic Progressions

Question

if the nth term of an AP is (2n+1) find the sum of first n terms
of the AP

Bluestar · Accepted Answer

The sum of n terms in an AP is given by
s= n/2(2a+(n-1)d)
where
s = sum of progression
n = number of terms
a = value of first term
d = difference between 2 terms

now, the first term in your question is 3 (2 x 1 +
1)
so, a = 3
second term is 5

third is 7, like that

so d = 2

Therefore, the sum of first n terms of the AP will
be

n/2 [2 x 3 + (n-1) 2]

simplifying, we get the sum as

n [3+n-1]

n (n+2)

thats all