Question

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

Answer 1

Let a be the first term and d be the common difference, then
a₅ = a + (5 - 1)d = a + 4d
a₇ = a + (7 - 1)d = a + 6d
a₅ + a₇ = a + 4d + a + 6d = 52
⇒ 2a + 10d = 52
⇒ a + 5d = 26                         ...(i)
Similarly,
a₁₀ = a + (10 – 1)d
= a + 9d
⇒ a + 9d = 46                         ...(ii)
Subtracting (i) from (ii),
4d = 20
⇒ d = `(20)/(4)` = 5
⇒ d = 5
Now, put the value of d in eq. (i)
a + 5 x 5 = 26
⇒ a = 26 – 25
⇒ a = 1
Hence,
a₂ = a₁ + d
= 1 + 5
= 6
a₃ = a₂ + d
= 6 + 5
= 11
a₄ = a₃ + d
= 11 + 5
= 16
∴ The A.P formed is 1, 6, 11, 16,….