Question

СРОЧНО,ЗАВТРА ЭКЗАМЕН, А Я НЕ В ЗУБ НОГОЙ,ПРОШУ выписаны первые несколько членов геометрической прогрессии :-6;-21;-73,5. найдите её четвёртый член!!!!!

Answer 1

Finding the Fourth Term of a Geometric Progression

To find the fourth term of a geometric progression, we need to determine the common ratio (r) and use it to calculate the fourth term.

In this case, we are given the first three terms of the geometric progression: -6, -21, and -73.5. To find the common ratio, we can divide any term by its preceding term.

Let's calculate the common ratio (r) using the given terms:

- For the second term, -21, divided by the first term, -6: r = -21 / -6 = 3.5

- For the third term, -73.5, divided by the second term, -21: r = -73.5 / -21 = 3.5

Since both divisions give us the same result of 3.5, we can conclude that the common ratio (r) is 3.5.

Now that we know the common ratio, we can use it to find the fourth term (a₄) of the geometric progression. We can use the formula:

a₄ = a₁ * r^(n-1)

where: - a₄ is the fourth term - a₁ is the first term - r is the common ratio - n is the position of the term we want to find (in this case, 4)

Let's substitute the values into the formula:

a₄ = -6 * 3.5^(4-1)

Now, let's calculate the fourth term:

a₄ = -6 * 3.5^3 = -6 * 42.875 = -257.25

Therefore, the fourth term of the geometric progression is -257.25.