Geometric Sequence Warmup 2

Given the rule: a_n = 7(½)^n-1

Identify the first term.

• a_n

• 7

• ½

• n

Answer explanation

The first term a_1 is found by substituting n=1 into the formula: a_1 = 7(½)^(1-1) = 7(½)^0 = 7(1) = 7. Thus, the first term is 7.

Tags

CCSS.HSF.BF.A.2

The rule for finding a_n of a geometric sequence is

a_n = 10(2)^n-1 _{What is the common ratio(r) of the sequence?}

• ²

• ¹⁰

• ²⁰

• 2ⁿ

Answer explanation

In a geometric sequence, the common ratio (r) can be found from the formula a_n = a_1 * r^(n-1). Here, a_1 = 10 and r = 2. Thus, the common ratio is 2, making the correct choice \(2\).

Tags

CCSS.HSF.BF.A.2

Given the explicit formula, find the first four terms:
a_n = -400(¹/₂)^n-1

• -400, -200, -100, -50

• -400, 200, -100, 50

• -400, -399.5, -399, -398.5

• -400, -300, -200, -100

Answer explanation

To find the first four terms of a_n = -400(1/2)^(n-1), calculate: a_1 = -400, a_2 = -200, a_3 = -100, a_4 = -50. Thus, the first four terms are -400, -200, -100, -50, which matches the correct answer choice.

Tags

CCSS.HSF.BF.A.2

What does r represent?

• Radical

• Common difference

• Common ratio

Answer explanation

In mathematics, r typically represents the common ratio in a geometric sequence, which is the factor by which each term is multiplied to get the next term. Therefore, the correct answer is 'Common ratio'.

Tags

CCSS.HSF.BF.A.2

What does a₁ represent?

• Any term

• First term

• Last term

Answer explanation

In mathematical notation, a₁ specifically denotes the first term of a sequence. Therefore, the correct answer is 'First term', as it accurately describes what a₁ represents.

Tags

CCSS.HSF.BF.A.2

What does n represent?

• Number

• Nothing

• Term you are trying to find

Answer explanation

In this context, n represents the 'Term you are trying to find', as it is commonly used in mathematics and programming to denote a variable or placeholder for an unknown value.

Tags

CCSS.6.EE.B.6