Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series: a₁ = 3, a_n = 3a_{n - 1} + 2 for all n > 1

Solution:

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

a₁ = 3, a_n = 3a_{n - 1} + 2 for all n > 1

a₂ = 3a₁ + 2 = 3(3) + 2 = 11

a₃ = 3a₂ + 2 = 3(11) + 2 = 35

a₄ = 3a₃ + 2 = 3(35) + 2 = 107

a₅ = 3a₄ + 2 = 3(107) + 2 = 323

Hence, the first five terms of the sequence are 3, 11, 35, 107, and 323.

The corresponding series is 3 + 11+ 35 + 107 + 323 + ....

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 Question 11

Write the first five terms of the following sequence and obtain the corresponding series: a₁ = 3, a_n = 3a_{n - 1} + 2 for all n > 1

Summary:

We had to find out the first five terms of the sequence where a₁ = 3, a_n = 3a_{n - 1} + 2 for all n > 1. Therefore the first five terms of the sequence are 3, 11, 35, 107, and 323