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In an arithmetic sequence, the first term,
a_(1), is equal to 9 , and the third term,
a_(3), is equal to 25 . 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 third term, $a_{3}$ , is equal to $25$ . 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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Find a value using two-variable equations: word problems

Full solution

Q. In an arithmetic sequence, the first term,

a_{1}

, is equal to

9

, and the third term,

a_{3}

, is equal to

25

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

\newline

d=5

\newline

d=6

\newline

d=7

\newline

d=8

Understand Arithmetic Sequence: Understand the properties of an arithmetic sequence. In an arithmetic sequence, each term after the first is obtained by adding a constant difference, $d$ , to the previous term. This means that the second term, $a_{2}$ , can be expressed as $a_{1} + d$ , and the third term, $a_{3}$ , can be expressed as $a_{1} + 2d$ .
Write Given Terms: Write down the given terms of the sequence. $\newline$ We are given that the first term $a_{1}$ is $9$ and the third term $a_{3}$ is $25$ .
Set Up Equation: Set up the equation for the third term using the first term and the common difference. $\newline$ We know that $a_{3} = a_{1} + 2d$ . Substituting the given values, we get $25 = 9 + 2d$ .
Solve for Common Difference: Solve for the common difference, $d$ . Starting with the equation $25 = 9 + 2d$ , we subtract $9$ from both sides to isolate the term with $d$ . $25 - 9 = 2d$ $16 = 2d$ Now, divide both sides by $2$ to solve for $d$ . $16 / 2 = d$ $8 = d$

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