Question

1. Найдите а) первый член; б) пятый член геометрической прогрессии, у которой знаменатель равен 5, а а седьмой член 62 500. можно с полным решением

Answer 1

Finding the First and Fifth Terms of a Geometric Progression

To find the first and fifth terms of a geometric progression, we need to know the common ratio and one of the terms. In this case, we are given that the common ratio is 5 and the seventh term is 62,500.

Let's denote the first term as a and the common ratio as r.

We can use the formula for the nth term of a geometric progression:

aₙ = a * r^(n-1)

Given that the seventh term is 62,500, we have:

a₇ = a * r^(7-1) = 62,500

Substituting the value of the common ratio, which is 5, we can solve for the first term:

a * 5^6 = 62,500

Simplifying the equation:

a * 15,625 = 62,500

Dividing both sides of the equation by 15,625:

a = 62,500 / 15,625 = 4

Therefore, the first term of the geometric progression is 4.

To find the fifth term, we can use the same formula:

a₅ = a * r^(5-1)

Substituting the values of the first term and the common ratio:

a₅ = 4 * 5^4

Simplifying the equation:

a₅ = 4 * 625 = 2,500

Therefore, the fifth term of the geometric progression is 2,500.

In summary: - The first term of the geometric progression is 4. - The fifth term of the geometric progression is 2,500.

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