Question

select the correct answer. which explicit function defines this arithmetic sequence? -351, -343, -335, -327, -319 a. f(n) = -8n + 359 b. f(n) = 8n - 351 c. f(n) = 8n - 359 d. f(n) = -8n - 351

Explanation:

Step1: Find common difference $d$

$d = -343 - (-351) = 8$

Step2: Identify first term $a_1$

$a_1 = -351$

Step3: Use arithmetic sequence formula

The explicit formula for an arithmetic sequence is $f(n) = a_1 + (n-1)d$. Substitute values:
$f(n) = -351 + (n-1) \times 8$
$f(n) = -351 + 8n - 8$
$f(n) = 8n - 359$

Step4: Verify with $n=2$

$f(2) = 8(2) - 359 = 16 - 359 = -343$, which matches the sequence.

Answer:

C. $f(n)=8n - 359$