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In an arithmetic sequence, the first term,
a_(1), is equal to 9 , and the sixth term,
a_(6), is equal to 39 . Which number represents the common difference of the arithmetic sequence?

d=5

d=6

d=7

d=8

In an arithmetic sequence, the first term, $a_{1}$ , is equal to $9$ , and the sixth term, $a_{6}$ , is equal to $39$ . Which number represents the common difference of the arithmetic sequence? $\newline$ $d=5$ $\newline$ $d=6$ $\newline$ $d=7$ $\newline$ $d=8$

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Evaluate two-variable equations: word problems

Full solution

Q. In an arithmetic sequence, the first term,

a_{1}

, is equal to

9

, and the sixth term,

a_{6}

, is equal to

39

. Which number represents the common difference of the arithmetic sequence?

\newline

d=5

\newline

d=6

\newline

d=7

\newline

d=8

Identify Given Terms: Identify the given terms in the arithmetic sequence. $\newline$ We are given the first term $a_{1}$ and the sixth term $a_{6}$ of the arithmetic sequence. The first term is $9$ , and the sixth term is $39$ .
Use Formula for nth Term: Use the formula for the nth term of an arithmetic sequence to find the common difference. $\newline$ The nth term of an arithmetic sequence is given by the formula $a_n = a_1 + (n - 1)d$ , where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.
Plug Known Values: Plug the known values into the formula to create an equation. $\newline$ We know that $a_{6} = 39$ , $a_{1} = 9$ , and $n = 6$ . We can substitute these values into the formula to find $d$ : $\newline$ $39 = 9 + (6 - 1)d$
Simplify and Solve: Simplify the equation and solve for $d$ . $39 = 9 + 5d$ $39 - 9 = 5d$ $30 = 5d$ $d = \frac{30}{5}$ $d = 6$

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