Math, asked by kalaisiva4132, 9 months ago

sum of first n terms of 2 APs are in the ratio n+7 : 3n+11 then the ratio of 9th term is

Answers

Answered by GujjarBoyy
2

Step-by-step explanation:

Let a

1

, a

2

be the first terms and d

1

, d

2

the common differences of the two given A.P.'s. Then, the sums of their n terms are given by

S

n

=

2

n

[2a

1

+(n−1)d

1

]

And,

S

n

=

2

n

[2a

2

+(n−1)d

2

]

Therefore,

S

n

S

n

=

2

n

[2a

2

+(n−1)d

2

]

2

n

[2a

1

+(n−1)d

1

]

=

2a

2

+(n−1)d

2

2a

1

+(n−1)d

1

It is given that

S

n

S

n

=

4n+27

7n+1

2a

2

+(n−1)d

2

2a

1

+(n−1)d

1

=

4n+27

7n+1

....(1)

To find the ratio of the mth terms of the two given AP's, we replace n by (2m-1) in equation 1.

Therefore,

2a

2

+(2m−2)d

2

2a

1

+(2m−2)d

1

=

4(2m−1)+27

7(2m−1)+1

a

2

+(m−1)d

2

a

1

+(m−1)d

1

=

8m+23

14m−6

Hence, the ratio of the mth terms of two AP's is (14m−6):(8m+23).

Similar questions