Question

If the ratio of nth terms of two AP's is (2n+8):(5n-3), then the ratio of the sum of their n terms is

(1). (2n+18):(5n+1)
(2). (5n-1):(2n+18)
(3). (2n+18):(5n-1)
(4). None of these.

...... ​

Answer 1

Given :  ratio of nth terms of two AP's is (2n+8):(5n-3),

To Find :  ratio of the sum of their n terms is

1). (2n+18):(5n+1)

(2). (5n-1):(2n+18)

(3). (2n+18):(5n-1)

(4). None of these.

Solution:

Sₙ = (n/2) ( first term + nth term )

aₙ  = 2n + 8

=> a₁  = 2(1) + 8  = 10

Sₙ = ( n/2)(10  + 2n + 8)   =  n ( n + 9)

aₙ  = 5n - 3

a₁  = 5(1) - 3  = 2

Sₙ = ( n/2)(2  + 5n -3)   =  n ( 5n -1 )/2

Ratio =   n ( n + 9) /  n ( 5n -1 )/2

= (2n + 18)/(5n - 1)

ratio of the sum of their n terms is (2n + 18)/(5n - 1)

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