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.OR4x4=16
Answer» For AP nth term isTn = a + (n-1)d Where,a = first termd = common difference T7 = a + 6dT3 = a + 2d T7/T3 = 12/5a + 6d/a + 2d = 12/55(a + 6d) = 12(a + 2d)5a + 30d = 12a + 24d12a - 5a = 30d - 24d7a = 6da = (6/7)d Ratio of 13th to 4th termT13/T4 = a + 12d/a + 3d Put value of a = (6/7)dT13/T4 = (6/7)d + 12d/(6/7)d + 3dT13/T4 = 90d/27d = 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.OR4x4=16

Answer»

For AP nth term isTn = a + (n-1)d

Where,a = first termd = common difference

T7 = a + 6dT3 = a + 2d

T7/T3 = 12/5a + 6d/a + 2d = 12/55(a + 6d) = 12(a + 2d)5a + 30d = 12a + 24d12a - 5a = 30d - 24d7a = 6da = (6/7)d

Ratio of 13th to 4th termT13/T4 = a + 12d/a + 3d

Put value of a = (6/7)dT13/T4 = (6/7)d + 12d/(6/7)d + 3dT13/T4 = 90d/27d = 10/3