Question

Please answer these two.its really very important to me

Answer 1

Answer:

(14m – 6) : (8m + 23)

From the picture, it looks both questions are same. So one solution for both.

Step-by-step explanation:

Sum of fist n terms of AP = n(a + (n – 1)d)/2

Where a is first term and d is common difference.

Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27)

Let us consider the first AP, first term is a and common difference is d.  

For the second AP, first term is x and common difference is y

The nth term of AP is given by a + (n – 1)d (a is first term and d is common difference.  

Rations of mth terms of both Aps is as follow

a + (m – 1)d : x + (m – 1)y  

Multiply both sides with 2, we get

= (2a + 2(m – 1)d) : (2x + 2(m – 1)y)

= (2a + {(2m – 1) – 1}d) : (2x + {(2m – 1) – 1}y)

That is same as sum of first 2m-1 terms of AP.  

Substituting 2m – 1 in the initial ratio of sum of first n terms, we get  (i.e. (7n+1):(4n+27))

= (7(2m – 1) + 1) : (4(2m – 1) +27)  

= (14m – 7 +1) : (8m – 4 + 27)

= (14m – 6) : (8m + 23)

Thus the ratio of mth terms of two AP’s is (14m – 6) : (8m + 23).