Find an explicit formula for the arithmetic sequence -5,13,31,49,dots.. Note: the first term should be b(1). b(n)=

Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence -5, 13, 31, 49, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Determine common difference: Determine the common difference (d) of the sequence by subtracting the first term from the second term. The common difference is 13 - (-5) = 18.Use explicit formula: Use the explicit formula for an arithmetic sequence, b(n) = b(1) + (n-1)d, where b(1) is the first term and d is the common difference. For the sequence -5, 13, 31, 49, ..., the first term, b(1), is -5 and the common difference, d, is 18.Write expression for sequence: Substitute the values of b(1) and d into the formula to write an expression to describe the sequence. The expression for the sequence -5, 13, 31, 49, ... is b(n) = -5 + (n-1) × 18.Simplify expression: Simplify the expression. b(n) = -5 + 18n - 18, which simplifies to b(n) = 18n - 23.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find an explicit formula for the arithmetic sequence
-5,13,31,49,dots.. Note: the first term should be
b(1).

b(n)=

Find an explicit formula for the arithmetic sequence $-5,13,31,49, \ldots$ .. Note: the first term should be $b(1)$ . $\newline$ $b(n)=$

View step-by-step help

Home

Math Problems

Algebra 2

Write a formula for an arithmetic sequence

Full solution

Q. Find an explicit formula for the arithmetic sequence

-5,13,31,49, \ldots

.. Note: the first term should be

b(1)

\newline

b(n)=

Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence $-5, 13, 31, 49, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Determine common difference: Determine the common difference $d$ of the sequence by subtracting the first term from the second term. The common difference is $13 - (-5) = 18$ .
Use explicit formula: Use the explicit formula for an arithmetic sequence, $b(n) = b(1) + (n-1)d$ , where $b(1)$ is the first term and $d$ is the common difference. For the sequence $-5, 13, 31, 49, \ldots$ , the first term, $b(1)$ , is $-5$ and the common difference, $d$ , is $18$ .
Write expression for sequence: Substitute the values of $b(1)$ and $d$ into the formula to write an expression to describe the sequence. The expression for the sequence $-5, 13, 31, 49, extellipsis$ is $b(n) = -5 + (n-1) imes 18$ .
Simplify expression: Simplify the expression. $b(n) = -5 + 18n - 18$ , which simplifies to $b(n) = 18n - 23$ .