Question

Формулы нахождения d и q Нужны формулы нахождения d и q в арифметической и геометрической прогрессиях, когда известно например a12 и a17.

Answer 1

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Answer 2

Formulas for Finding d and q in Arithmetic and Geometric Progressions

In arithmetic and geometric progressions, the formulas for finding the common difference (d) and the common ratio (q) can be derived based on the given terms of the sequence.

Arithmetic Progression: The general formula for finding the common difference (d) in an arithmetic progression is: d = a_n - a_m

Where: - a_n is the nth term - a_m is the mth term

Geometric Progression: The general formula for finding the common ratio (q) in a geometric progression is: q = a_n / a_m

Where: - a_n is the nth term - a_m is the mth term

Example with a₁₂ and a₁₇:

Let's consider the terms a₁₂ and a₁₇ in both arithmetic and geometric progressions.

Arithmetic Progression: For an arithmetic progression, the common difference (d) can be found using the formula: d = a₁₇ - a₁₂

Geometric Progression: For a geometric progression, the common ratio (q) can be found using the formula: q = a₁₇ / a₁₂

These formulas allow for the determination of the common difference and common ratio in both arithmetic and geometric progressions based on the given terms.

If you have any further questions or need additional assistance, feel free to ask!