Question

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if the ratio of first n terms of 2 AP's is (7n+1):(4n+27) then ratio of their. mth term is:1)) (7m +1):(4m+27)
2). (14m -6):(8m+23)
3). (6m-8):(8m+14)
4).(8m+6):(14m+8)
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Answer 1

Question : If the ratio of first n terms of 2 AP's is (7n+1) : (4n+27) , then ratio of their mth term = ?

Answer : Opt. 2

Refer the attachment after following the given steps.

Let's assume that the first terms of the A.P is a1 , a2 and common difference is d1 , d2.

Also, Let the sum of n terms of given A.P's be Sn1 and Sn2.

Now,

As per your question,

$\tt{\frac{Sn_1}{Sn_2}}$ = ${\frac{7n+1}{4n + 27}}$

Using the formula for Sum of n terms,

$\tt{\frac{ \frac{n}{2} (2a _{1} + (n - 1)d_{1}) }{\frac{n}{2} (2a _{2} + (n - 1)d_{2})} = \frac{7n + 1}{4n + 27}}$

Cancelling (n/2) on L.H.S,

$\tt{\frac{ (2a _{1} + (n - 1)d_{1}) }{(2a _{2} + (n - 1)d_{2})} = \frac{7n +1 }{4n + 27}}$

$=> \tt {\frac{a_{1} + ( \frac{n - 1}{2} )d _{1} }{{a_{2} + ( \frac{n - 1}{2} )d _{2} } } = \frac{7n + 1}{4n + 27}}$

We have to find the ratio of their mth terms.

.°. Putting (n-1)/2 = m - 1

For next steps , refer the attachment.

Final answer :

Opt. 2 ) (14m -6):(8m+23) is the answer to the question.

________________________

Answer 2

Answer:

Option(2)

Step-by-step explanation:

Let a₁,d₁ be the first term and the common difference of the first AP.

Let a₂,d₂ be the first term and the common difference of the second AP.

Given, ratio of first n terms of 2 A'P is (7n + 1) : (4n + 27).

The remaining answer is explained in the attachment.