Question

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

1, 4, 7, 10, … ,88

Answer 1

Given A.P = 1, 4, 7, 10, … ,88

Here, a = 1 and d = (4 – 1) = 3

Now, find the number of terms when the last term is known i.e, 88

a_n = 1 + (n – 1)3 = 88

1 + 3n – 3 = 88

3n = 90

n = 30

Hence, the A.P has 30 terms.

So, the 12^th term from the end is same as (30 – 12 + 1)^th of the A.P which is the 19^th term.

⇒ a₈₉ = 1 + (19 – 1)3

= 1 + 18(3)

= 1 + 54

= 55

Therefore, the 12^th term from the end of the A.P is 55.