Math, asked by Faeka9382, 1 year ago

The ratio of the sum of n terms of two aps is (4n+2):(3n+47). Find the ratio of their 9th term

Answers

Answered by komalmittal147
9

Here's ur answer dear.

The answer is absolutely right.

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Answered by JeanaShupp
2

The ratio of 9th term is 5: 7

Step-by-step explanation:

Given : The ratio of n terms of two A.P. is (4n+2):(3n+47)

To find: The ratio of 9th term

As we know the sum of n terms of an A.P. is

S_n=\dfrac{n}{2}(2a+(n-1)d )

where  a is first term , d is common difference and n is number of terms of an A.P.

Now let  a and d are the first term and common difference of 1st A.P. and a' and d' is the first term and common difference of 2nd A.P.

According to question we have

\dfrac{S_{n1}}{S_{n2}}= \dfrac{\dfrac{n}{2}(2a+(n-1)d) }{\dfrac{n}{2}(2a'+(n-1)d')}  \\\\\\\Rightarrow \dfrac{4n+2}{3n+47} = \dfrac{2a+(n-1)d }{2a'+(n-1)d'}  \\\\\\\Rightarrow \dfrac{4n+2}{3n+47} = \dfrac{a+\dfrac{(n-1)d}{2}  }{a'+\dfrac{(n-1)d'}{2}  }

Now for 9th term put n = 19

we get

\\\\\Rightarrow \dfrac{4\times 17+2}{3\times 17+47} = \dfrac{a+\dfrac{(17-1)d}{2}  }{a'+\dfrac{(17-1)d'}{2}  }\\\\\Rightarrow \dfrac{70}{98} = \dfrac{a+8d}{a'+8d'} \\\\\Rightarrow \dfrac{5}{7} =\dfrac{a_9}{a'_9}

Hence the ratio of 9th term is 5: 7

#Learn more

The ratio of the 5th and 3rd terms of an A.P. is 2:5. Find the ratio of the 15th and 7th term.

brainly.in/question/8446073

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