2.7 Warm Up [DISC] 11.07.24

Front

What is the formula for the nth term of a linear recurrence relation?

Back

The nth term of a linear recurrence relation can be expressed as a_n = c * a_(n-1) + d, where c and d are constants.

Front

How do you find the first few terms of a sequence defined by a recurrence relation?

Back

To find the first few terms, start with the initial condition and apply the recurrence relation iteratively.

Front

What is a geometric series?

Back

A geometric series is a series of terms where each term after the first is found by multiplying the previous term by a constant called the common ratio.

Front

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

Back

The sum S_n of the first n terms of a geometric series can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

Front

What is the formula for the sum of an arithmetic series?

Back

The sum S_n of the first n terms of an arithmetic series can be calculated using the formula S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by, denoted as d.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the significance of the initial term in a sequence?

Back

The initial term is crucial as it serves as the starting point for generating subsequent terms in the sequence.

Front

How do you determine if a series converges or diverges?

Back

A series converges if the sum of its terms approaches a finite limit; it diverges if the sum grows without bound or does not approach a limit.

Front

What is the relationship between sequences and series?

Back

A sequence is an ordered list of numbers, while a series is the sum of the terms of a sequence.