Question

find common diff / ratio with missing te
question
in an arithmetic sequence, the first term, $a_1$, is equal to 3, and the sixth term, $a_6$, is equal to 23. which number represents the common difference of the arithmetic sequence?
answer
$d = 2$
$d = 3$
$d = 4$
$d = 5$

Explanation:

Step1: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1+(n - 1)d\), where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.

Step2: Substitute known values

We know \(a_1 = 3\), \(n = 6\), and \(a_6 = 23\). Substitute these into the formula: \(23=3+(6 - 1)d\).

Step3: Solve for \(d\)

Simplify the equation: \(23=3 + 5d\). Subtract 3 from both sides: \(23-3=5d\), so \(20 = 5d\). Divide both sides by 5: \(d=\frac{20}{5}=4\).

Answer:

\(d = 4\) (corresponding to the option \(d = 4\))