Question

Find the 10th term from the end of the AP 4, 9, 14, ..., 254.
Or, which term of the AP 24, 21, 18, 15, ... is the first negative term?

Answer 1

Here, a = 4, d = (9 - 4) = 5, l = 254 and n = 10
Now, n^th term from the end = {l - (n - 1)d}
∴ 10^th term from the end = {254 - (10 - 1) × 5}
= {254 - (9 × 5)} = (254 - 45) = 209
Hence, the 10^th term from the end is 209.

OR
Here, a = 24, d = (21 - 24) = - 3
Let the n^th term of the given AP be the first negative term.
Then, T_n < 0 ⇒ {a+ (n - 1)d} < 0
⇒ { 24 + (n - 1) × ( - 3) < 0
⇒ (27 - 3n) < 0
⇒ 27 < 3n
⇒ 3n > 27
⇒ n > 9
∴ n = 10
Hence, the 10^th term is the first negative term of the given AP.