ARITHMETIC SEQUENCE-SERIES-MEAN

(EASY ROUND)

1. It is a function whose domain is a set of consecutive integers. If a domain is not specified, it is understood that the domain starts with 1.

• SEQUENCE

• SERIES

• ARITHMETIC

• MEAN

Answer explanation

(EASY ROUND)

2. It is a sequence wherein the terms are generated by adding a constant number called common difference.

• Arithmetic Series

• Arithmetic Mean

• Arithmetic Sequence

Answer explanation

Arithmetic sequences

An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.

(EASY ROUND)

3. Is the sequence arithmetic: -3, 3, -3, 3, ...

• NO

• YES

Answer explanation

Is the sequence arithmetic: -3, 3, -3, 3, ...

The given sequence is not arithmetic since it has no common difference or pattern.

(EASY ROUND)

4. Refers to the terms between any two nonconsecutive terms of an arithmetic sequence.

• Arithmetic Series

• Arithmetic Mean

• Arithmetic Sequence

Answer explanation

Arithmetic Mean: The terms between any two nonconsecutive terms of an arithmetic sequence.

(EASY ROUND)

5. This formula is used for finding _________

Answer explanation

Ann arithmetic series is simply the sum of the terms of an arithmetic sequence. More specifically, the sum of the first \large\color{red}{n}n terms in an arithmetic sequence is called the partial sum. The partial sum is denoted by the symbol \large{{S_n}}Sn​.

(AVERAGE ROUND)

1. Which of the the following are examples of arithmetic sequence?

• 5, 11, 16, 21

Answer explanation

1/2, 1, 3/2, 5/2 is an arithmetic sequence with common difference 1/2.

(AVERAGE ROUND)

2. How many squares are there in Diagram 6

Answer explanation

Diagram 1: 3 squares

Diagram 2: 5 squares

Diagram 3: 7 squares

Diagram 4: 9 squares

Diagram 5: 11 squares

Diagram 6: 13 squares

(ACERAGE ROUND)

3. Find the 125^th term in the arithmetic sequence 4, −1, −6, −11, …

• -613

• -616

• -619

Answer explanation

(AVERAGE ROUND)

4. If x+1, x+5 and 3x+1 are in arithmetic sequence, what is the value of x?

Answer explanation

If x+1, x+5 and 3x+1 are in arithmetic sequence, what is the value of x?

Solution:

2nd term - 1st term

= x+5-(x+1)

= x+5-x-1

= 5-1

= 4

(AVERAGE ROUND)

5. Write the explicit rule for this situation.

• f(n) = 35 + 3(n − 1)

• f(n) = 3 + 35(n − 1)

• f(n) = 35 −3(n − 1)

Answer explanation

f(n) = 35 −3(n − 1)

f(1) = 35-3(1-1) = 35

f(2) = 35-3(2-1) = 35-3 = 32

f(3) = 35-3(3-1) = 35-6 = 29

f(4) = 26

f(5) = 23