Sequences and Series

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Tags

CCSS.HSF.BF.A.2

Front

What is a series?

Back

A series is the sum of the terms of a sequence.

Tags

CCSS.HSA.SSE.B.4

Front

Define an arithmetic sequence.

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Tags

CCSS.HSF.BF.A.2

Front

Define a geometric sequence.

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term (a_n) can be calculated using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the sum of the first n terms of an arithmetic series?

Back

The sum (S_n) can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

How do you find the sum of the first n terms of a geometric series?

Back

The sum (S_n) can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.

Tags

CCSS.HSA.SSE.B.4

Front

What is the binomial theorem?

Back

The binomial theorem describes the algebraic expansion of powers of a binomial. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k = 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What does 'n choose k' mean in combinatorics?

Back

'n choose k' (denoted as C(n, k) or nCk) represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.

Tags

CCSS.HSA.APR.C.5