Question

an arithmetic sequence is given below.
31, 24, 17, 10, ...
write an explicit formula for the ( n^{\text{th}} ) term ( a_n ).
( a_n = square )

Explanation:

Step1: Identify first term $a_1$

The first term of the sequence is $a_1 = 31$.

Step2: Calculate common difference $d$

Find the difference between consecutive terms:
$d = 24 - 31 = -7$

Step3: Apply arithmetic sequence formula

The explicit formula for the $n^\text{th}$ term of an arithmetic sequence is $a_n = a_1 + (n-1)d$. Substitute $a_1=31$ and $d=-7$:
$a_n = 31 + (n-1)(-7)$
Simplify the expression:
$a_n = 31 -7n +7 = 38 -7n$

Answer:

$a_n = 38 - 7n$