Question

Знайдіть 51-й член арифметичної прогресії (), якщо: =52, d = -3.

Answer 1

Ответ:

$a_{n} = a_{1} + d(n - 1)$

$a_{51} = 52 + ( - 3)(51 - 1) \\ a_{51} = 52 - 3 \times 50 \\ a_{51} = 52 - 150 \\ a_{51} = - 98$

Answer 2

Finding the 51st Term of an Arithmetic Progression

To find the 51st term of an arithmetic progression, we can use the formula:

nth term (Tn) = a + (n - 1)d

Where: - a = the first term - n = the term number - d = the common difference

Given: - a = 52 - d = -3 - n = 51

Calculation

Plugging the given values into the formula:

T51 = 52 + (51 - 1)(-3)

Solving this equation gives us the 51st term of the arithmetic progression. Let's calculate it.

Solution

T51 = 52 + (51 - 1)(-3) T51 = 52 + 50(-3) T51 = 52 - 150 T51 = -98

So, the 51st term of the arithmetic progression is -98.