Write the first five terms of the sequences whose n^th term is a_n = (- 1)^{n - 1} 5^{n + 1}

Solution:

nth term is given as a_n = (- 1)^{n - 1} 5^{n + 1}

Substituting n = 1, 2, 3, 4, 5

a₁ = (- 1)^{1 - 1} 5^{1 + 1} = 5² = 25

a₂ = (- 1)^{2 - 1} 5^{2 + 1} = - 5³ = - 125

a₃ = (- 1)^{3 - 1} 5^{3 + 1} = 5⁴ = 625

a₄ = (- 1)^{4 - 1} 5^{4 + 1} = - 5⁵ = - 3125

a₅ = (- 1)^{5 - 1} 5^{5 + 1} = 5⁶ = 15625

Therefore, the required terms are 25, - 125, 625, - 3125, and 15625

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 Question 5

Write the first five terms of the sequences whose n^th term is a_n = (- 1)^{n - 1} 5^{n + 1}

Summary:

The questions tells us that the nth term is a_n = (- 1)^{n - 1} 5^{n + 1}. Therefore the terms are 25, - 125, 625, - 3125 and 15625