Question 1

Which of the following describes a geometric sequence?

Accepted Answer

Each term is obtained by multiplying the previous term by the same number.

Answer

The terms are arranged in alphabetical order.

Answer

The increase between terms is random.

Answer

The difference between consecutive terms is constant.

Question 2

Why is the sequence 4, 8, 16, 32, ... classified as a geometric sequence?

Accepted Answer

It doubles every term.

Answer

It increases by 4 each time.

Answer

It follows no pattern.

Answer

It decreases by 2 each time.

Question 3

Consider the following sequences: Sequence X: 15, 20, 25, 30, ... Sequence Y: 2, 6, 18, 54, ... Which statement is correct?

Accepted Answer

Sequence X is arithmetic, while Sequence Y is geometric.

Answer

Sequence X is geometric, while Sequence Y is arithmetic.

Answer

Both sequences are arithmetic.

Answer

Both sequences are geometric.

Question 4

A sequence starts at 18 and increases by 6 every term. Find the 12th term. Two learners solved the problem. Learner X; a12=18+6(12)     Learner Y;  a12=18+6(12−1) Who solved the problem incorrectly?

Accepted Answer

Learner X because 6 must be multiplied to 11 only;

Answer

Neither learner because the sequence is geometric.

Answer

Learner Y because the common difference is added 11 times.

Answer

Both learners used the correct formula.

Question 5

A learner claims that the 9th term of the arithmetic sequence 20, 24, 28, 32, ... is 56. How should the answer be evaluated?

Accepted Answer

Incorrect because the correct 9th term is 52.

Answer

Correct because 56 is divisible by 4.

Answer

Incorrect because the sequence is geometric.

Answer

Correct because the sequence is increasing.

Question 6

A student solves the following problem: "A population of rabbits triples every month. If there are 150 rabbits at the beginning, how many rabbits will there be after 5 months?" The student writes: 150+3(5) How should the solution be evaluated?

Accepted Answer

Incorrect because tripling requires repeated multiplication.

Answer

Correct because 3 is the growth rate.

Answer

Correct because the months represent the term number.

Answer

Incorrect because rabbit populations cannot be represented by sequences.

Question 7

Which statement correctly distinguishes a sequence from a series?

Accepted Answer

A sequence is an ordered list of terms, while a series is the sum of those terms.

Answer

A series is simply another name for a sequence.

Answer

A sequence always involves multiplication.

Answer

A series only applies to geometric patterns.

Question 8

Which of the following situations represents a series?

Accepted Answer

Finding the total number of steps walked during the week.

Answer

Listing the number of steps walked each day.

Answer

Ranking students according to their scores.

Answer

Recording the daily temperature for one week.

Question 9

What type of series is represented by the given pattern: ₱1,200, ₱1,350, ₱1,500, ₱1,650, ₱1,800, ...?

Accepted Answer

Arithmetic series

Answer

Harmonic series

Answer

Geometric series

Answer

Fibonacci series

Question 10

During a school fund-raising activity, the Mathematics Club records the amount collected from students. The first week's collection was ₱500. The amount collected increased by 20% each week, forming the pattern:

₱500, ₱600, ₱720, ₱864, ₱1,036.80, …

The club wants to represent the collected amounts as a series and use mathematical notation to describe the pattern.

What type of series is represented by the given pattern? What is the common ratio of the series?

A. Arithmetic series B. Geometric series C. Harmonic series D. Fibonacci series

Accepted Answer

Geometric series; Common ratio is 1.2

Answer

Geometric series; Common ratio is 0.2

Answer

Arithmetic series; Common difference is 100

Answer

Arithmetic series; Common difference is 120

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