# Find the Sum of the Following Arithmetic Progressions: (X - Y)/(X + Y),(3x - 2y)/(X + Y), (5x - 3y)/(X + Y) .....To N Terms - Mathematics

Find the sum of the following arithmetic progressions:

(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y),  .....to n terms

#### Solution

(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y),  .....to n terms

Number of terms (n) = n

Number of terms (n)n = ((x - y)/(x + y))

Common difference of the A.P. (d)  = a_2 - a_1

= ((3x - 2)/(x + y)) - (x - y)/(x + y)

= ((3x - 2y) - (x - y))/(x +y)

= (3x - 2y - x + y)/(x + y)

= (2x - y)/(x - y)

So using the formula we get

S_n = n/2[2((x - y)/(x + y)) + (n - 1)((2x - y )/(x + y))]

= (n/2) [((2x - 2y)/(x + y)) + (n(2x - y)- 2x + y)/(x + y)]

= (n/2)[(2x -2y)/(x + y) + (((n (2x - y) - 2x + y))/(x + y))]

Now, on further solving the above equation we get,

= (n/2)((2x - 2y + n(2x - y) - 2x + y)/(x + y))

= (n/2) ((n(2x - y) - y)/(x + y))

Therefore, the sum of first n terms for the given A.P. is (n/2) ((n(2x - y) - y)/(x + y))

Concept: Sum of First n Terms of an AP
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 1.7 | Page 30