Question

Найти шестой член геометрической прогрессии 64;-48;36

Answer 1

Решение задания смотри на фотографии

Answer 2

Finding the Sixth Term of a Geometric Progression

To find the sixth term of a geometric progression, we need to know the first term and the common ratio. In this case, the given geometric progression is 64, -48, 36.

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

The formula to find the nth term of a geometric progression is:

aₙ = a × r^(n-1)

We are looking for the sixth term, so n = 6.

Now, let's substitute the given values into the formula:

a₆ = 64 × r^(6-1)

Simplifying the exponent:

a₆ = 64 × r^5

To find the value of r, we can use the ratio between the second and first terms of the geometric progression:

r = (-48) / 64

Simplifying:

r = -3/4

Now, substituting the value of r into the formula:

a₆ = 64 × (-3/4)^5

Simplifying the exponent:

a₆ = 64 × (-3/4)^5 = 64 × (-243/1024)

Calculating the value:

a₆ = -15

Therefore, the sixth term of the geometric progression 64, -48, 36 is -15.