Find the 15th term from end for A.P., 10, 15, 20, 25, 30, ..., 1000.

Formula Used.

d_n = a_{n + 1} – a_n

a_n = a + (n–1)d

In the above sequence,

a = 10;

d₁ = a₂–a₁ = 15–10 = 5

d₂ = a₃–a₂ = 20–15 = 5

d₃ = a₄–a₃ = 25–20 = 5

The difference in sequence is same and comes to be (5).

As the last term is 1000

a_n = a + (n–1)d

1000 = 10 + (n–1)5

1000 = 10 + 5n–5 = 5 + 5n

5n = 995

n = = 199^th term

15 term from the end will be

199 + 1–15 = 185^th term

a_n = a + (n–1)d

a₁₈₅ = 10 + (185–1)5

= 10 + 184×5

= 10 + 920

= 930