Q52. Find first five terms of the seq... [FREE SOLUTION]

91影视

Chapter 14: Q52. (page 768)

Find first five terms of the sequence in which $a_{1} = 3, a_{n + 1} = 2 a_{n} + 5$ .

Short Answer

Expert verified

The first five terms of the sequence are $3, 11, 27, 59 and 123$ .

Step by step solution

Step 1. Write down the given information.

The given sequence has $a_{1} = 3 鈥� and a_{n + 1} = 2 a_{n} + 5$ .

Step 2. Evaluating first five terms of the given sequence.

Since, the first term is $a_{1} = 3$ of the given sequence. Therefore, the remaining four terms can be obtained by plugging $n = 1, 2, 3, 4$ to get $a_{2}, a_{3}, a_{4} and a_{5}$ in the given sequence $a_{n + 1} = 2 a_{n} + 5$ .

For $n = 1$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(1) + 1} = 2 a_{(1)} + 5.... (For n = 1) \\ a_{2} = 2 (3) + 5.... (鈭� a_{1} = 3) \\ a_{2} = 11 \end{matrix}$

For $n = 2$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(2) + 1} = 2 a_{(2)} + 5.... (For n = 2) \\ a_{3} = 2 (11) + 5.... (鈭� a_{2} = 11) \\ a_{3} = 27 \end{matrix}$

For $n = 3$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(3) + 1} = 2 a_{(3)} + 5.... (For n = 3) \\ a_{4} = 2 (27) + 5.... (鈭� a_{3} = 27) \\ a_{4} = 59 \end{matrix}$

For $n = 4$ ,

$\begin{matrix} a_{n + 1} = 2 a_{n} + 5.... (Given) \\ a_{(4) + 1} = 2 a_{(4)} + 5.... (For n = 4) \\ a_{5} = 2 (59) + 5.... (鈭� a_{4} = 59) \\ a_{5} = 123 \end{matrix}$

Since, $a_{1} = 3, a_{2} = 11, a_{3} = 27, a_{4} = 59 and a_{5} = 123$ . Therefore, the first five terms of the sequence are $3, 11, 27, 59 and 123$ .

Step 3. Conclusion.

The first five terms of the sequence are $3, 11, 27, 59 and 123$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find first five terms of the sequence in which $a_{1} = 3, a_{n + 1} = 2 a_{n} + 5$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Evaluating first five terms of the given sequence.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Calculus

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Find first five terms of the sequence in which a1=3,an+1=2an+5.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Evaluating first five terms of the given sequence.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Calculus

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find first five terms of the sequence in which $a_{1} = 3, a_{n + 1} = 2 a_{n} + 5$ .