Find the 10th term from end for A.P., 3, 6, 9, 12, ... 300.

Formula Used.

d_n = a_{n + 1} – a_n

a_n = a + (n–1)d

In the above sequence,

a = 3;

d₁ = a₂–a₁ = 6–3 = 3

d₂ = a₃–a₂ = 9–6 = 3

d₃ = a₄–a₃ = 12–9 = 3

The difference in sequence is same and comes to be (3).

As the last term is 300

a_n = a + (n–1)d

300 = 3 + (n–1)3

300 = 3 + 3n–3 = 3n

n = = 100^th term

10^th term from the end is

100 + 1–10 = 91^st term

∵ while counting, last term is also counted

a_n = a + (n–1)d

a₉₁ = 3 + (91–1)3

= 3 + 90×3

= 273