Question

The ratio of 7th to the 3rd term of an AP is 12:5 .Find the ratio of 13th to 4th term

Answer 1

Answer:

Step-by-step explanation:

now 7th term=a +6d

3rd term=a+2d_eq1

multiply eq1 whith 3

we get 3a +6d.Now subtract it with

Answer 2

7th term, A7 = a + ( 7 - 1) d

A7 = a + 6d

3rd term, A3 = a + ( 3 - 1 ) d

A3 = a +2d

Given, A7/A3 = 12/5

( a + 6d ) / ( a +2d) = 12 /5

5a + 30 d = 12a + 24 d

30d - 24 d = 12 a - 5a

6d = 7a

d = 7a/6

13th term, A13 = a + ( 13 - 1) d = a + 12d

4th term, A4 = a + ( 4 - 1) d = a + 3d

Ratio of A13/A4 = ( a + 12d ) / ( a +3d )

Putting value of "d",

A13/A4 = [ a + 12(7a/6)] /[ a + 3( 7a/6)]

A13/A4 = [a + 14a ] / [ a + (7a/2)]

A13/A4 = ( a + 14a ) / ( 9a/2 )

A13/A4 = 15a / 9a/2

A13/A4 = 10/3

$\fbox{Ratio \:=\: 10\: :\: 3}$