Question

If A=B then find the ratio of Sn:tn

Answer 1

Hi there,

The question says A=B.This does not help us to find the ratio of Sn:tn as required. Therefore, I think the correct question should be as follows:

If a = d. then find the ratio of Sn:tn.

Answer: Sn : tn  = a(n+1)/2n

Step-by-step explanation:

Here, we are given, the first term “a” = the common difference “d”.

So, firstly, we will calculate for the last term “tn”.

∴ tn = a + (n-1)d  

⇒ tn = a + nd – d  

⇒ tn = a + na – a …… [∴ a = d]

⇒ tn = na ……. (i)

Now, secondly, we will calculate for the sum of first n terms i.e., “Sn”.

∴ Sn = a/2 [2a + (n-1)d]  

⇒ Sn = a/2 [2a + (a-1)a]  

⇒ Sn = a/2 [2a + a² - a]

⇒ Sn = a/2 [a(n+1)] ……. (ii)

Dividing eq. (ii) by (i), we get

Sn : tn  

= [a/2 {a(n+1)}] / [na]  

= a(n+1)/2n