Q. 18

# If there are (2n + 1) terms in an arithmetic series, then prove that the ratio of the sum of odd terms to the sum of even terms is (n + 1) : n.

In the A.P, let

First term = a

Common difference = d

Number of terms = (2n + 1)

Series: a,a + d,a + 2d……a + 2nd

For Odd terms

: a, a + 2d,…a + 2nd

First term = a

Common difference = 2d

Number of terms = n + 1

Sum of terms =

Sum of odd terms =

Sum of odd terms =

For Even terms

: a + d, a + 3d,…a + (2n–1)d

First term = a + d

Common difference = 2d

Number of terms = n

Sum of terms =

Sum of even terms =

Sum of even terms =

Sum of odd terms : Sum of even terms = : =

Sum of odd terms : Sum of even terms = (n + 1) : n

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