Question

write a linear equation that represents the arithmetic sequence 10, 8, 6, 4, ...
a) $a_n = 2+10(n - 1)$
b) $a_n = 10 + 2(n + 1)$
c) $a_n = 10-2(n - 1)$
d) $a_n = 10+2(n - 1)$
question 16 (5 points)
which of the following is equivalent to $sum_{k = 0}^{5}a_k$?
a) $a_1 + a_2+a_3+a_4+a_5$
b) $a_1 + a_2+a_3+ldots+a_{infty}$
c) $a_0 + a_1+a_2+a_3+a_4+a_5$

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 and $d$ is the common difference.

Step2: Identify $a_1$ and $d$

For the sequence $10,8,6,4,\cdots$, $a_1 = 10$ and $d=8 - 10=-2$.

Step3: Substitute into the formula

Substitute $a_1 = 10$ and $d=-2$ into $a_n=a_1+(n - 1)d$, we get $a_n=10+(n - 1)(-2)=10-2(n - 1)$.

For the second question:

Step1: Recall the meaning of the sum notation

The sum $\sum_{k = 0}^{5}a_k$ means $a_0+a_1+a_2+a_3+a_4+a_5$.

Answer:

First question: C. $a_n = 10 - 2(n - 1)$
Second question: C. $a_0 + a_1 + a_2 + a_3 + a_4 + a_5$