Question

If the ratio of the sum of first of term of two AP is (7x+1)(4x+2)find the ratio of the terms​

Answer 1

Answer:

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Step-by-step explanation:

Let the two series' be T nand T n′  with first terms a and a ′and common differences d and d ′

The ratio of the sums of the series' S

n

​

 and S

n

′

​

 is given as,

S

n

′

​

S

n

​

​

=

[n/2][2a

′

+[n−1]d

′

]

[n/2][2a+[n−1]d]

​

=

4n+27

7n+1

​

Or,

a

′

+[(n−1)/2]d

′

a+[(n−1)/2]d

​

=

4n+27

7n+1

​

 ...(1)

We have to find,

T

11

′

​

T

11

​

​

=

a

′

+10d

′

a+10d

​

Choosing (n−1)/2=10 or n=21 in (1) we get

​

T11=

a+10d =

4(21)+27

7(21)+1

​

= 111148

​

ratio= 4:3