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

1.	37. The ratio of 7th to the 3rd term of an AP is 12:5. Find the ratio of 13th to the 4th term.OR484
Answer» Formula of n th term in AP = a+(n-1)d Where a is the first term n is the term number d is the common ratio Now when n = 7 So,a+(7-1)d=a+6d When n = 3 So, a+(3-1)d=a+2d Since we are given that the ratio of 7th to 3rd term of an AP is 12:5 ⇒(a + 6d)/(a + 2d) = 12/5 ⇒5a+30d=12a+24d ⇒6d = 7a ⇒a=6d/7 Now 13th term =a+(13-1)d =a+12d = 6d/7 + 12d 4th term =a+(4-1)d =a+3d = 6d/7 + 3d Now ratio of 13th and 4th term (6d/7 + 12d)/(6d/7 + 3d)= (6d + 84)/(6d + 21d)= 90d/27d= 10/3= 10:3 Thus the ratio of the 13th and 4th term is 10:3

37. The ratio of 7th to the 3rd term of an AP is 12:5. Find the ratio of 13th to the 4th term.OR484

Answer»

Formula of n th term in AP = a+(n-1)d

Where a is the first term

n is the term number

d is the common ratio

Now when n = 7

So,a+(7-1)d=a+6d

When n = 3

So, a+(3-1)d=a+2d

Since we are given that the ratio of 7th to 3rd term of an AP is 12:5

⇒(a + 6d)/(a + 2d) = 12/5

⇒5a+30d=12a+24d

⇒6d = 7a

⇒a=6d/7

Now 13th term =a+(13-1)d =a+12d = 6d/7 + 12d

4th term =a+(4-1)d =a+3d = 6d/7 + 3d

Now ratio of 13th and 4th term

(6d/7 + 12d)/(6d/7 + 3d)= (6d + 84)/(6d + 21d)= 90d/27d= 10/3= 10:3

Thus the ratio of the 13th and 4th term is 10:3