Question

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

3,8,13, … ,253

Answer 1

Given A.P = 3,8,13, … ,253

Here, a = 3 and d = (8 – 3) = 5

Now, find the number of terms when the last term is known i.e, 253

a_n = 3 + (n – 1)5 = 253

3 + 5n – 5 = 253

5n = 253 + 2 = 255

n = 255/5

n = 51

Hence, the A.P has 51 terms.

So, the 12^th term from the end is same as (51 – 12 + 1)^th of the A.P which is the 40^th term.

⇒ a₄₀ = 3 + (40 – 1)5

= 3 + 39(5)

= 3 + 195

= 198

Therefore, the 12^th term from the end of the A.P is 198.