An A.P consists of 60 terms. If the first and the last terms be 7 and 125respectively, find 32 ^ndterm.

Given: n = 60

T ₁ = 7
T ₆₀ = 125

We know that,

T _n = a + (n – 1)d

⇒ T ₁ = a + (1 – 1)d = a = 7

And,

⇒ T ₆₀ = a + (60 – 1)d

⇒ T ₆₀ = a + 59d = 125
⇒ T ₆₀ = 7 + 59d = 125
⇒ 59d = 125 – 7 = 118
T ₃₂ = a ₁ + (32 – 1)d = a ₁ + 31d = 7 + 31(2) = 7 + 62
Hence, T ₃₂ = 69.