Question

is this sequence arithmetic or geometric? 9, 36, 144, 576,...
question 29 (1 point) what do we mean when we say a₁?
question 30 (1 point) both pi and the golden ratio are irrational numbers.

Explanation:

Step1: Check for arithmetic - common difference

Find the differences between consecutive terms: $36 - 9=27$, $144 - 36 = 108$. Since $27
eq108$, there is no common difference, so it's not arithmetic.

Step2: Check for geometric - common ratio

Find the ratios between consecutive terms: $\frac{36}{9}=4$, $\frac{144}{36}=4$, $\frac{576}{144}=4$. Since there is a common ratio of 4, the sequence is geometric.

Step3: Define $a_1$

In a sequence denoted as $a_n$, $n = 1,2,\cdots$, $a_1$ represents the first - term.

Step4: Recall irrational numbers

$\pi\approx3.14159\cdots$ and the golden ratio $\varphi=\frac{1 + \sqrt{5}}{2}\approx1.618\cdots$ are both non - repeating, non - terminating decimals, so they are irrational numbers.

Answer:

Question 28: B. Geometric
Question 29: B. the first term
Question 30: True