Question

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

Answer 1

Let the first term and common difference of AP are a and d, respectively.

According to the question,

a₅ + a₇ = 52 and a₁₀ = 46

⇒ a + (5 – 1)d + a + (7 – 1)d = 52  ...[∵ a_n = a + (n – 1)d]

And a + (10 – 1)d = 46

⇒ a + 4d + a + 6d = 52

And a + 9d = 46

⇒ 2a + 10d = 52

And a + 9d = 46

⇒ a + 5d = 26   ...(i)

a + 9d = 46   ...(ii)

On subtracting equation (i) from equation (ii), we get

4d = 20

⇒ d = 5 

From equation (i),

a = 26 – 5(5) = 1

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,...