A2 Lessons 1.1 to 1.4 Review

Identify whether the following sequence is arithmetic, geometric or neither. If possible, find the common difference, d, or the common ratio, r. Sequence: 5, 10, 15, 20, ...

• The sequence is arithmetic with a common difference d = 5.

• The sequence is geometric with a common ratio r = 2.

• The sequence is neither arithmetic nor geometric.

• The sequence is geometric with a common ratio r = 3.

Answer explanation

The sequence increases by 5 each time (10-5=5, 15-10=5, etc.), indicating it is arithmetic. The common difference is d = 5.

Tags

CCSS.HSF.BF.A.2

Identify whether the following sequence is arithmetic, geometric or neither. If possible, find the common difference, d, or the common ratio, r. Sequence: 800, 560, 392, 274.4, ...

• The sequence is geometric with a common ratio r = 0.7.

• The sequence is arithmetic with a common difference d = -240.

• The sequence is neither arithmetic nor geometric.

• The sequence is geometric with a common ratio r = 0.5.

Answer explanation

The sequence is geometric because each term is multiplied by a common ratio of 0.7 to get the next term (560/800 = 0.7, 392/560 = 0.7, etc.). Thus, the correct choice is that the sequence is geometric with r = 0.7.

Tags

CCSS.HSF.BF.A.2

A portion of a sequence is shown in the table. The terms continue to decrease at the same rate according to the pattern shown. Find the value of a₁.

• a₁ = 10

• a₁ = 3

• a₁ = -4

• a₁ = 1

Answer explanation

The sequence increases consistently by 7. To go backward from the second term, subtract 7. The first term is 3.

Tags

CCSS.HSF.BF.A.2

A portion of a sequence is shown in the table. The terms continue to grow at the same rate according to the pattern shown. Write an explicit formula for the sequence.

• a_n = 7n - 4

• a_n = 7n + 3

• a_n = 5n + 2

• a_n = 6n + 1

Answer explanation

The sequence increases by 7 for each term. The first term is 7. The explicit formula is a_n = 3 + 7(n-1). This can be simplified by distributing the 7 and getting a_n = 3 + 7n -7. If you combine like terms, you get a_n = 7n - 4.

Tags

CCSS.HSF.BF.A.2

Maria starts a job with a yearly salary of $35,000. She earns an additional $3,000 each year after that. If Maria stays at this job for 25 years, what will be the total amount she earns over the 25-year period?

• $1,775,000

• $142,000

• $3,550,000

• $1,812,500

Answer explanation

Maria's salary increases by $3,000 each year. Over 25 years, her total earnings are calculated as follows: $35,000 + $3,000(25-1) = $107,000. The sum of her earnings after 25 years can be found by using the sum formula. S_25 = 25/2($35000 + $107,000) = $1,775,000.

Tags

CCSS.HSF.BF.A.2

Write the expression as a sum of terms.

• (4×1-5) + (4×2-5) + (4×3-5) + ... + (4×8-5)

  = -1 + 3 + 7 + 11 + 15 + 19 + 23 + 27

• (4×1+5) + (4×2+5) + (4×3+5) + ... + (4×8+5)

  = 9 + 13 + 17 + 21 + 25 + 29 + 33 + 37

• (4×1-5) + (4×2-5) + (4×3-5) + ... + (4×8-5)

  = -4 + 0 + 4 + 8 + 12 + 16 + 20 + 24

• (4×1-5) + (4×2-5) + (4×3-5) + ... + (4×8-5)

  = 1 + 5 + 9 + 13 + 17 + 21 + 25 + 29

Answer explanation

The correct choice simplifies the expression (4×n-5) for n=1 to 8, resulting in the sequence -1, 3, 7, 11, 15, 19, 23, 27. This matches the first answer choice, confirming it as the correct representation.

Tags

CCSS.HSF.BF.A.2

Calculate the sum.

• 30

• 128

• 2

• 160

Answer explanation

To find the sum, add the terms.

(4×1-5) + (4×2-5) + (4×3-5) + ... + (4×8-5)

= -1 + 3 + 7 + 11 + 15 + 19 + 23 + 27

= 128

The recursive formula below defines a sequence.
a₁ = 3
aₙ = 4(aₙ₋₁)
Is the sequence arithmetic, geometric, or neither?

If possible, identify the common difference or common ratio.

• The sequence is geometric with a common ratio of 4.

• The sequence is arithmetic with a common difference of 4.

• The sequence is neither arithmetic nor geometric.

• The sequence is geometric with a common ratio of 3.

Answer explanation

The sequence is defined recursively with a₁ = 3 and aₙ = 4(aₙ₋₁). This indicates each term is obtained by multiplying the previous term by 4, confirming it is geometric with a common ratio of 4.

Tags

CCSS.HSF.BF.A.2

The recursive formula below defines a sequence.
b₁ = 2
bₙ = 5(bₙ₋₁).

What are the first 4 terms of this sequence?

• 2, 10, 50, 250

• 2, 7, 12, 17

• 2, 4, 8, 16

• 2, 12, 72, 432

Answer explanation

The sequence starts with b₁ = 2. The formula bₙ = 5(bₙ₋₁) tells us to multiply by 5 to build the sequence. (2*5=10, 10*5 = 50, etc.) Thus, the first four terms are 2, 10, 50, 250.

Tags

CCSS.HSF.BF.A.2

The recursive formula below defines a sequence.
a₁ = 3
aₙ = 4(aₙ₋₁).

Write an explicit formula for the sequence.

• aₙ = 3 × 4ⁿ⁻¹

• aₙ = 4 × 3ⁿ⁻¹

• aₙ = 3 × 4ⁿ

• aₙ = 4 × 3ⁿ

Answer explanation

The recursive formula aₙ = 4(aₙ₋₁) indicates that each term is 4 times the previous term, so this is a geometric sequence. Starting with a₁ = 3 and r = 4, the explicit formula aₙ = 3 × 4ⁿ⁻¹.

Tags

CCSS.HSF.BF.A.2