Question

Hey.
Can anyone please answer this question?

Answer 1

Answer:

3n : 25

25

____

3

4.3

***n= 4.3

plz follow me

mark me as brilliest

Answer 2

Given :

• Ratio of sum of n terms of two AP's = (7n + 1) : (4n + 27)

To Find :

• The ratio of their mth terms.

Solution :

First AP :

Let the first term be ${a_1}$

Let the common difference be ${d_1}$

${S_n}$ of first AP :

$\mathtt{S_{n}\:=\:{\dfrac{n}{2}}}$ $\mathtt{2a_1\:+\:(n-1)\:d_{1}}$ ---> (i)

Second AP :

Let the first term be ${a_2}$

Let the common difference be ${d_2}$

${S_n}$ of second AP :

➟ $\mathtt{S_{n}'\:=\:{\dfrac{n}{2}}}$ $\mathtt{2a_{2}\:+\:(n-1)\:d_{2}}$ ---> (ii)

Ratio of ${S_n}$ of first AP and second AP is given as :

• (7n + 1) : (4n + 27)

➟ $\frac{\frac{n}{2}\:(2a_{1}\:+\:(n-1)\:d_{1}}{{\frac{n}{2}\:(2a_{2}\:+\:(n-1)\:d_{2}}}$ =$\mathtt{\dfrac{7n+1}{4n+27}}$

➟ $\mathtt{\dfrac{2a_1\:+\:(n-1)\:d_1}{2a_2\:+\:(n-1)\:d_2}}$ =$\mathtt{\dfrac{7n+1}{4n+27}}$

Replace n by 2m-1,

➟ $\sf{\dfrac{2a_1\:+\:(2m-1-1)\:d_1}{2a_2\:+\:(2m-1-1)\:d_2}}$=$\sf{\dfrac{7n+1}{4n+27}}$

➟ $\mathtt{\dfrac{2a_1\:+\:(2m-2)\:d_1}{2a_2\:+\:(2m-2)\:d_2}}$=$\mathtt{\dfrac{7(2m-1)+1}{4(2m-1) +27}}$

➟ $\mathtt{\dfrac{2a_1\:+\:(2m-2)\:d_1}{2a_2\:+\:(2m-2)\:d_2}}$=$\mathtt{\dfrac{(14m\:-7)+1}{(8m-4) +27}}$

➟ $\mathtt{\dfrac{a_1\:+\:(m-1)\:d_1}{2a_2\:+\:(m-1)\:d_2}}$ = $\mathtt{\dfrac{(14m\:-6)}{8m\:+23}}$

Hence, ratio :

$\bold{\mathtt{\boxed{\dfrac{a_1\:+\:(m-1)\:d_{1}}{2a_{2}\:+\:(m-1)\:d_{2}}}}}$ = $\bold{\mathtt{\boxed{\dfrac{14m\:-6}{8m\:+23}}}}$