Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: a₁ = a₂ = 2, a_n = a^{n - 1} - 1, n > 2

Solution:

The sequence is a list of numbers (or items) that exhibits a particular pattern.

a₁ = a₂ = 2, aⁿ = a^{n - 1} - 1, n > 2

⇒ a₃ = a₂ - 1 = 2 - 1 = 1

a₄ = a₃ - 1 = 1 - 1 = 0

a₅ = a₄ - 1 = 0 - 1 = - 1

Hence, the first five terms of the sequence are 2, 2, 1, 0 and - 1

The corresponding series is 2 + 2 + 1 + 0 + (- 1) + ....

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 Question 13

Write the first five terms of the following sequence and obtain the corresponding series: a₁ = a₂ = 2, a_n = a^{n - 1} - 1, n > 2

Summary:

It is given that the sequence is a₁ = a₂ = 2, a_n = a^{n - 1} - 1, n > 2. Therefore, the first five terms are 2, 2, 1, 0 and - 1