Question

find the 12 term of AP 3, 5, 7. . . . . . . ​

Answer 1

Given A.P = 3, 5, 7, 9, …. 201

Here, a = 3 and d = (5 – 3) = 2

Now,

find the number of terms when the last term is

known i.e,

201 an

= 3 + (n – 1)2

= 201 3 + 2n – 2

= 201 2n

= 200 n

= 100

Hence, the A.P has 100 terms.

So, the 12th term from the end is same as (100 – 12 + 1)th of the A.P which is the 89th term.

⇒ a89 = 3 + (89 – 1)2

= 3 + 88(2)

= 3 + 176

= 179

Therefore, the 12th term from the end of the A.P is 179.