The sum of the 5th and the 7th terms of an AP is 52 and the 10th term

1.	The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.
Answer» Let the first term, common difference be a and d respectively. As we know a_n = a + (n - 1)d and Given a₅ + a₇ = 52 a + 4d + a + 6d = 52 2a + 10d = 52 a + 5d = 26 a = 26 - 5d [ eqn i] also we have given a₁₀ = 46 a + 9d = 46 26 - 5d + 9d = 46 [ from eqn i] 4d = 46 - 26 4d = 20 d = 5 using this value in eqn I , we get a = 26 - 5d a = 26 - 5(5) a = 1 as a = 6 and d = 5 So, required AP is a, a + d, a + 2d, a + 3d, …. i.e., 1, 1 + 5, 1 + 2(5), 1 + 3(5), …. i.e., 1, 6, 11, 16, …

The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

Answer»

Let the first term, common difference be a and d respectively.

As we know

a_n = a + (n - 1)d

and Given

a₅ + a₇ = 52

a + 4d + a + 6d = 52

2a + 10d = 52

a + 5d = 26

a = 26 - 5d [ eqn i]

also we have given

a₁₀ = 46

a + 9d = 46

26 - 5d + 9d = 46 [ from eqn i]

4d = 46 - 26

4d = 20

d = 5

using this value in eqn I , we get

a = 26 - 5d

a = 26 - 5(5)

a = 1

as a = 6 and d = 5

So, required AP is a, a + d, a + 2d, a + 3d, …. i.e., 1, 1 + 5, 1 + 2(5), 1 + 3(5), …. i.e., 1, 6, 11, 16, …