Question

If the nth terms of the two A.g.s 9, 7, 5, … and 24, 21, 18, … are the same, find the value of n. Also, find that term

Answer 1

nth term of two A.P.s 9, 7, 5,… and 24, 21, 18, … are same
In the first A.P. 9, 7, 5, …
a = 9 and d = 7 – 9 = –2
T_n = a + (n – 1)d
= 9 + (n – 1)(–2)
= 9 – 2n + 2
= 11 – 2n
and in second A.P. 24, 21, 18,...
a₁ = 24, d₁ = 21 – 24 = –3
T_n = 24 + (n – 1)(–3)
= 24 – 3n + 3
= 27 – 3n
∵ The nth terms of both A.P. is same
∴ 11 – 2n = 27 – 3n
–2n + 3n = 27 – 11
⇒ n = 16
and
T₁₆ = a + (n – 1)d
= 9 + 15 x (–2)
= 9 – 30
= –21.