Math, asked by optimusprime59, 1 year ago

the ratio of 6th and 8th term of an A.P is 7:9 find the ratio of 9th term to 13th term​


Anonymous: ___k off

Answers

Answered by snehagupta24
64

Answer:

5:7

Step-by-step explanation:

let 6th term= 7x and 8th term= 9x

a+5d= 7x-----------1

a+7d= 9x ------2

subtracting 2 from 1

-2d= -2x

d= x

7x= a+5x

a= 2x

9th term: 13th term

a+ 8d : a+12d

2x + 8x : 2x+ 12x

10x: 14x

5:7


aalia37: how the 5d come
Answered by ColinJacobus
54

Answer:  The required ratio of the 9th term to 13th term is 5 : 7.

Step-by-step explanation:  Given that the ratio of 6th and 8th term of an A.P is 7 : 9.

We are to find the ratio of 9th term to 13th term.

We know that

the n-th term of an A.P. with first term a and common difference d is given by

a_n=a+(n-1)d.

According to the given information, we have

a_6:a_8=7:9\\\\\\\Rightarrow \dfrac{a_6}{a_8}=\dfrac{7}{9}\\\\\\\Rightarrow \dfrac{a+(6-1)d}{a+(8-1)d}=\dfrac{7}{9}\\\\\Rightarrow9(a+5d)=7(a+7d)\\\\\Rightarrow 9a+45d=7a+49d\\\\\Rightarrow 9a-7a=49d-45d\\\\\Rightarrow 2a=4d\\\\\Rightarrow a=2d~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Therefore, the ratio of the 9th term to 13 term will be

a_9:a_{13}\\\\\\=\dfrac{a_9}{a_{13}}\\\\\\=\dfrac{a+(9-1)d}{a+(13-1)d}\\\\\\=\dfrac{a+8d}{a+12d}\\\\\\=\dfrac{2d+8d}{2d+12d}~~~~~~~~~~~~~~[\textup{using equation (i)}]\\\\\\=\dfrac{10d}{14d}\\\\\\=\dfrac{5}{7}\\\\=5:7.

Thus, the required ratio of the 9th term to 13th term is 5 : 7.

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