Question

Consider the arithmetic sequence: 6, 2, -2, -6, \dots6,2,−2,−6,…6, comma, 2, comma, minus, 2, comma, minus, 6, comma, dots If nnn is an integer, which of these functions generate the sequence? Choose all answers that apply: Choose all answers that apply:

Answer 1

Answer:

$a_n=-4n+10$

Step-by-step explanation:

Let us consider the given terms one by one:

First term, $a$ = 6

Second term, $a_2=2$

Difference between First and Second term = 2 - 6 = -4

Third term, $a_3$ = -2

Difference between Second and Third term = -2 - 2 = -4

Fourth term, $a_4$ = -6

Difference between Second and Third term = -6 -(-2) = -4

Therefore, the common difference is:

$d$ = -4

Let the use the formula for $n^{th}$ term of an arithmetic sequence:

$a_n=a+(n-1)d$

Putting the values of $a$ and $d$:

$a_n=6+(n-1)(-4)\\\Rightarrow a_n=6-4n+4\\\Rightarrow a_n=-4n+10$

Therefore, the $n^{th}$ term is:

$a_n=-4n+10$

Answer 2

Answer:

on khan academy, b! goooood luck! :D

Step-by-step explanation: