Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find an explicit formula for the arithmetic sequence 
-11,-3,5,13,dots.
Note: the first term should be 
b(1).

b(n)=

Find an explicit formula for the arithmetic sequence\newline11,3,5,13, -11,-3,5,13, \ldots \text {. } \newlineNote: the first term should be b(1) b(1) .\newlineb(n)= b(n)=\square

Full solution

Q. Find an explicit formula for the arithmetic sequence\newline11,3,5,13, -11,-3,5,13, \ldots \text {. } \newlineNote: the first term should be b(1) b(1) .\newlineb(n)= b(n)=\square
  1. Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence 11-11, 3-3, 55, 1313, ... has a common difference between consecutive terms, so it is an arithmetic sequence.
  2. Find common difference: Determine the common difference dd of the sequence by subtracting any term from the term that follows it. For example, the difference between the second term 3-3 and the first term 11-11 is 3(11)=8-3 - (-11) = 8.
  3. Use explicit formula: Use the explicit formula for an arithmetic sequence, b(n)=b(1)+(n1)db(n) = b(1) + (n-1)d, where b(1)b(1) is the first term and dd is the common difference. For this sequence, the first term, b(1)b(1), is 11-11 and the common difference, dd, is 88.
  4. Write expression for sequence: Substitute the values of b(1)b(1) and dd into the formula to write an expression to describe the sequence. The expression for the sequence 11,3,5,13,extellipsis-11, -3, 5, 13, extellipsis is b(n)=11+(n1)imes8b(n) = -11 + (n-1) imes 8.
  5. Simplify expression: Simplify the expression to find the explicit formula. b(n)=11+8n8b(n) = -11 + 8n - 8, which simplifies to b(n)=8n19b(n) = 8n - 19.

More problems from Write a formula for an arithmetic sequence