Find an explicit formula for the arithmetic sequence 37,74,111,148,dots.. Note: the first term should be a(1). a(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 37, 74, 111, 148, ... has a common difference between consecutive terms, so it is an arithmetic sequence.Determine First Term and Common Difference: Determine the first term (a1) and the common difference (d) of the sequence. The first term is 37. To find the common difference, subtract the first term from the second term: 74 - 37 = 37.Use Explicit Formula: Use the explicit formula for an arithmetic sequence, an = a1 + (n-1)d, where a1 is the first term and d is the common difference. For this sequence, a1 = 37 and d = 37.Write Expression for Sequence: Substitute the values of a1 and d into the formula to write an expression to describe the sequence. The expression for the sequence is an = 37 + (n-1) × 37.Simplify Expression: Simplify the expression. an = 37 + 37n - 37 simplifies to an = 37n.

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
37,74,111,148,dots..
Note: the first term should be
a(1).

a(n)=

Find an explicit formula for the arithmetic sequence $\newline$ $37,74,111,148, \ldots$ $\newline$ Note: the first term should be $a(1)$ . $\newline$ $a(n)=$

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

\newline

37,74,111,148, \ldots

\newline

Note: the first term should be

a(1)

\newline

a(n)=

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence $37, 74, 111, 148, extellipsis$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Determine First Term and Common Difference: Determine the first term ( $a_1$ ) and the common difference ( $d$ ) of the sequence. The first term is $37$ . To find the common difference, subtract the first term from the second term: $74 - 37 = 37$ .
Use Explicit Formula: Use the explicit formula for an arithmetic sequence, $a_n = a_1 + (n-1)d$ , where $a_1$ is the first term and $d$ is the common difference. For this sequence, $a_1 = 37$ and $d = 37$ .
Write Expression for Sequence: Substitute the values of $a_{1}$ and $d$ into the formula to write an expression to describe the sequence. The expression for the sequence is $a_{n} = 37 + (n-1) \times 37$ .
Simplify Expression: Simplify the expression. $a_n = 37 + 37n - 37$ simplifies to $a_n = 37n$ .