Find If 5 Is in the Arithmetic Sequence: Solve 2n - 1

2n1 2n-1

Is the number 5 a term in the above sequence?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Is the number 5 part of the sequence?
00:10 We'll plug 5 into the sequence formula, and solve for N.
00:15 If N is a positive whole number, it tells us the position of 5.
00:21 Let's focus on solving for N now.
00:36 Great! That's how we find our answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

2n1 2n-1

Is the number 5 a term in the above sequence?

2

Step-by-step solution

To determine if the number 5 is a term in the sequence given by an=2n1 a_n = 2n - 1 , we need to find a positive integer n n such that 2n1=5 2n - 1 = 5 .

Let's solve the equation:

1. Start with the equation: 2n1=5 2n - 1 = 5

2. Add 1 to both sides to isolate the term involving n n : 2n=6 2n = 6

3. Divide both sides by 2 to solve for n n : n=3 n = 3

Since n=3 n = 3 is a positive integer, the number 5 is indeed a term in the sequence. Therefore, the correct answer is Yes.

3

Final Answer

Yes

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations