Question

Find the 69^th term of the G.P. 1, -1, 1, -1, ...

Answer 1

In the given G.P., we have t₁ = 1, t₂ = –1, t₃ = 1 and t₄ = –1.
Thus, we have the first term, i.e., a = t₁ = 1, and the common ratio, i.e., $r=\frac{t_2}{t_1}=\frac{-1}{1}=-1$.
We know that the n^th term of the G.P. is t_n = ar^{n – 1}.
By taking a = 1, r = –1 and n = 69, we have:
t₆₉ = (1)(–1)^{69 – 1}
$\Rightarrow$ t₆₉ = (1)(–1)⁶⁸
$\Rightarrow$ t₆₉ = 1 × 1 = 1
Thus, the 69^th term is 1.