The 9th term exceeds the fifth term of an AP by 32. The sum of the ninth and fifth terms is 114. Find the eight term of the AP.?

T₉ = a + (9 - 1)d = a + 8d
T₅ = a + (5 - 1)d = a + 4d
T₉ - T₅ = 32
⇒ (a + 8d) - (a + 4d) = 32
⇒ 4d = 32
∴ d = 8
T₉ + T₅ = (a + 8d) + (a + 4d)
= 2a + 12d
T₉ + T₅ = 114
⇒ 114 = 2(a + 6d)
⇒ a + 6d = 57
∴ T₈ = a + 7d
= a + 6d + d
= 57 + 8 = 65