What is the difference between a sequence and a series in IB DP Mathematics?

In IB DP Mathematics, a sequence is an ordered list of numbers following a specific pattern, while a series is the sum of the terms of a sequence. For example, in the sequence 2, 4, 6, 8, the series would be the sum 2 + 4 + 6 + 8.

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

To find the nth term of an arithmetic sequence, use the formula: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference between consecutive terms. This formula helps in identifying any term in the sequence based on its position.

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

The sum of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where S_n is the sum of the series, n is the number of terms, a_1 is the first term, and a_n is the nth term. This formula is crucial for solving problems involving the total of a sequence of numbers.

How do you determine if a sequence is geometric?

A sequence is geometric if the ratio between consecutive terms is constant. This constant ratio is called the common ratio, denoted as r. For example, in the sequence 3, 6, 12, 24, the common ratio is 2, as each term is obtained by multiplying the previous term by 2.

What is the formula for the sum of a geometric series?

The sum of the first n terms of a geometric series is given by the formula: S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum, a_1 is the first term, r is the common ratio, and n is the number of terms. This formula is applicable when the common ratio r is not equal to 1.

Sequences and SeriesIB DP Mathematics (166711)

Sequence and Series

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