Number Series: Arithmetic and Geometric Progressions

14 Questions

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

an = a1 + (n-1)d

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

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

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

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

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

an = ar^(n-1)

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

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

Sn = n/2[2a1 + (n-1)d]

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

Toddlerhood

What is a primary focus of development during early childhood?

Social skills and emotional regulation

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

Adolescence

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

Adulthood

What is a key aspect of development during middle childhood?

Refining social skills and developing friendships

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

Young Adulthood

What is a primary concern during older adulthood?

Maintaining physical and mental health

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, ...