Question

What is the n^th term of the sequence 25, -125, 625, -3125, …….?
1. (-5)^{2n - 1}
2. (-1)²ⁿ5ⁿ⁺¹
3. (-1)^{2n – 1} 5ⁿ⁺¹
4. (-1)^n-1 5ⁿ⁺¹
5. None of these

Answer 1

Correct Answer - Option 4 : (-1)^n-1 5ⁿ⁺¹

Concept:

If a₁, a₂, …., a_n is a GP then the general term is given by: a_n = a × r^{n - 1} where a is the 1^st term and r is the common ratio.

Calculation:

Given: 25, -125, 625, -3125, …….

Here, first term a = 25 and common ratio r = -5.

As we know that, if a₁, a₂, …., a_n is a GP then the general term is given by: a_n = a × r^{n - 1} where a is the first term and r is the common ratio.

⇒ The general term is : a_n = 25 × (-5)^{n – 1} = (-1)^{n – 1} × 5^{n + 1}