An A.P. consists

Given: a = 7, n = 60 and l = a₆₀ = 125

We know, a_n = a + (n – 1)d where a is first term or a₁ and d is common difference and n is any natural number

When n = 60:

∴ a₆₀ = a + (60 – 1)d

⇒ a₆₀ = a + 59d

When n = 32:

∴ a₃₂ = a + (32 – 1)d

⇒ a₃₂ = a + 31d …………(i)

According to question:

a₆₀ = 125

⇒ a + 59d = 125

⇒ 7 + 59d = 125

⇒ 59d = 125 – 7

⇒ 59d = 118

⇒ d = 2

Now put the value of a = 7 and d = 2 in a₃₂

⇒ a₃₂ = a + 31d………(From (i))

⇒ a₃₂ = 7 + 31(2)

⇒ a₃₂ = 7 + 62

⇒ a₃₂ = 69

Hence, 32^thterm of the given A.P. is 69