Question

the ratio of the 5th and 3rd terms of an AP is 5:2. Find the ratio of the 15th and 7th terms

Answer 1

Answer:

Let a is the first term and d is the common difference of the AP

Now, given T5 : T3 = 2 : 5

=> T5 / T3 = 2 / 5

=> {a + (5 - 1)d}/{a + (3 - 1)d} = 2/5

=> {a + 4d}/{a + 2d} = 2/5

=> 5{a + 4d} = 2{a + 2d}

=> 5a + 20d = 2a + 4d

=> 5a - 2a = 4d - 20d

=> 3a = -16d

=> a = -16d/3

Now, T15 / T7 = {a + (15 - 1)d}/{a + (7- 1)d}

=> T15 / T7 = {a + 14d}/{a + 6d}

=> T15 / T7 = {-16d/3 + 14d}/{-16d/3 + 6d}

=> T15 / T7 = {(-16d/2 + 42d)/3}/{(-16d + 18d)/3}

=> T15 / T7 = {26d/3}/{2d/3}

=> T15 / T7 = 26d/2d

=> T15 / T7 = 13/1

=> T15 : T7 = 13 : 1