An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
Given: a = 7, n = 60 and l = a60 = 125
We know, an = 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, 32thterm of the given A.P. is 69