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Number Series: Arithmetic and Geometric Progressions

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Number Series: Arithmetic and Geometric Progressions

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Questions and Answers

What is the formula for the nth term of an Arithmetic Progression?

an = a1 + (n-1)d (correct)

an = a1 - (n-1)d

an = a1 - nd

an = a1 + nd

What is the common characteristic of the sequences 2, 5, 8, 11,... and 10, 15, 20, 25,...?

Each term is obtained by adding a fixed constant to the previous term (correct)

Each term is obtained by subtracting a fixed constant from the previous term

Each term is obtained by dividing the previous term by a fixed constant

Each term is obtained by multiplying the previous term by a fixed constant

What is the formula for the sum of a Geometric Progression?

Sn = a(1 - r^n) / (1 - r) (correct)

Sn = a(1 + r^n) / (1 + r)

Sn = a(1 + r^n) / (1 - r)

Sn = a(1 - r^n) / (1 + r)

What is the difference between any two consecutive terms in an Arithmetic Progression?

d Signup and view all the answers

What is the formula for the nth term of a Geometric Progression?

an = ar^(n-1) Signup and view all the answers

What is the common characteristic of the sequences 2, 6, 18, 34,... and 10, 20, 40, 80,...?

Each term is obtained by multiplying the previous term by a fixed constant Signup and view all the answers

What is the formula for the sum of an Arithmetic Progression?

Sn = n/2[2a1 + (n-1)d] Signup and view all the answers

At what stage of human life do individuals typically begin to assert their independence and test boundaries?

Toddlerhood Signup and view all the answers

What is a primary focus of development during early childhood?

Social skills and emotional regulation Signup and view all the answers

Which stage of human life is characterized by the physical changes of puberty?

Adolescence Signup and view all the answers

At what stage do individuals typically take on responsibilities and leadership roles?

Adulthood Signup and view all the answers

What is a key aspect of development during middle childhood?

Refining social skills and developing friendships Signup and view all the answers

At what stage of human life do individuals typically focus on establishing independence and self-sufficiency?

Young Adulthood Signup and view all the answers

What is a primary concern during older adulthood?

Maintaining physical and mental health Signup and view all the answers

Study Notes

Number Series

Arithmetic Progressions (AP)

Definition: A sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.
Formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Characteristics:
- Each term is obtained by adding a fixed constant (d) to the previous term.
- The difference between any two consecutive terms is constant (d).
- The sum of an AP can be calculated using the formula: Sn = n/2[2a1 + (n-1)d].
Examples:
- 2, 5, 8, 11, ...
- 10, 15, 20, 25, ...

Geometric Progressions (GP)

Definition: A sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant.
Formula: an = ar^(n-1), where an is the nth term, a is the first term, r is the common ratio, and n is the term number.
Characteristics:
- Each term is obtained by multiplying the previous term by a fixed constant (r).
- The ratio of any two consecutive terms is constant (r).
- The sum of a GP can be calculated using the formula: Sn = a(1 - r^n) / (1 - r).
Examples:
- 2, 6, 18, 34, ...
- 10, 20, 40, 80, ...

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Description

Test your understanding of number series, including arithmetic progressions and geometric progressions, with their formulas, characteristics, and examples.