Question

Find the 12^th term from the end of the arithmetic progressions:

3, 5, 7, 9, …. 201

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

a_n = 3 + (n – 1)2 = 201

3 + 2n – 2 = 201

2n = 200

n = 100

Hence, the A.P has 100 terms.

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

⇒ a₈₉ = 3 + (89 – 1)2

= 3 + 88(2)

= 3 + 176

= 179

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