Question

Find the sum of an ap (x-2y),(2x-y),3x.......(11x+8y)

Answer 1

Question:-

Find the sum of an AP

(x-2 y) , (2 x-y) , 3 x , ............ , (11 x+8 y)

Solution:-

given that :

• first term, a = x - 2 y
• common difference, d = 2 x - y - (x - 2y) = x + y
• last term , l = aₙ = 11 x + 8 y

aₙ = a + ( n-1) d

11 x + 8 y = x - 2 y + ( n - 1) (x + y)

10 x + 10 y = n - 1 ( x + y)

10 ( x + y ) = n - 1 ( x + y )

n - 1 = 10

n = 11  

now,

we have to find

Sₙ = n/2 * ( a + l )

Sₙ = 11 / 2 * ( x - 2 y + 11 x + 8 y )

Sₙ = 11 / 2 * ( 12 x + 6 y )

Sₙ = 11 * ( 6 x + 3 y )

Sₙ = 66 x + 33 y       ( Ans.)