Question

if the sum of n termsvof two arithmetic progression are in the ratio 3n+5/5n+7, then their nth terms are in the ratio ​

Answer 1

     

In the ratio 3n + 5 : 5n + 7, if you put the value of n as 2n - 1, then you'll get the ratio of nth terms.

So taking n as 2n - 1,

3(2n - 1) + 5 : 5(2n - 1) + 7

⇒ 6n - 3 + 5 : 10n - 5 + 7

⇒ 6n + 2 : 10n + 2

⇒ 3n + 1 : 5n + 1

So this is the answer.

So remember this that, if the ratio of sums of two APs are in the ratio an + b : cn + d, then put the value of n as 2k - 1  to find the ratio of kth terms.

Plz ask me if you've any doubts.

Thank you. :-))

   

Answer 2

Answer:

3n+1 / 5n+1

Step-by-step explanation:

When you've gotta find the mth term when the AP is n, you replace it with 2m-1 right?

Similarly replace the n of the sum with 2n-1

So 3n+5/5n+7

=3(2n-1)+5/5(2n-1)+7

=6n+2/10n+2

=3n+1/5n+1

Well.. quite simple now innit?

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