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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) = \(\square\)

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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) = \(\square\)

Identify Type of Sequence: Identify whether the given sequence is geometric or arithmetic. The sequence $37, 74, 111, 148, \ldots$ has a common difference between consecutive terms, so it is an arithmetic sequence.
Find First Term and Common Difference: Determine the first term ( $a_1$ ) and the common difference ( $d$ ) of the sequence. The first term $a_1$ is $37$ . To find the common difference, subtract the first term from the second term: $d = 74 - 37 = 37$ .
Apply 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. Substitute the values of $a_1$ and $d$ into the formula. The expression for the sequence is $a_n = 37 + (n-1) \times 37$ .
Simplify Expression: Simplify the expression by distributing the $37$ inside the parentheses. $a_n = 37 + 37n - 37$ . Combine like terms to get the final expression.
Final Explicit Formula: After combining like terms, the final expression is $a_n = 37n$ . This is the explicit formula for the given arithmetic sequence.

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