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 (a)  

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

(a)  

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?

(a)  

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