Question

Геометрическая прогрессия. Нужно найти b5, S4. b2=15 , b3=25!!! помогите

Answer 1

Geometric Progression

A geometric progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The general form of a geometric progression is:

a, ar, ar^2, ar^3, ar^4, ...

Where: - a is the first term - r is the common ratio

To find the value of b5 in the geometric progression, we need to know the values of b2 and b3. In this case, b2 = 15 and b3 = 25.

To find the common ratio r, we can use the formula:

r = b3 / b2

Substituting the given values, we have:

r = 25 / 15

Simplifying, we find that r = 5/3.

Now, we can find the value of b5 using the formula:

b5 = b2 * r^3

Substituting the values we have:

b5 = 15 * (5/3)^3

Calculating this expression, we find that b5 ≈ 125.

Sum of the First Four Terms (S4)

To find the sum of the first four terms (S4) in the geometric progression, we can use the formula:

S4 = a * (1 - r^4) / (1 - r)

Substituting the values we have:

S4 = 15 * (1 - (5/3)^4) / (1 - 5/3)

Calculating this expression, we find that S4 ≈ 171.67.

Therefore, in the given geometric progression, b5 ≈ 125 and S4 ≈ 171.67.

Please let me know if there's anything else I can help you with!