Question

геометрическая прогрессия bn задана условиями b1=4 Bn+1=2bn, Найдите b7Ответ должен получить 256 но это не точно

Answer 1

$b_1=4\\ b_{n+1}=2\cdot b_n\\ q=\frac{b_{n+1}}{b_n}=\frac{2b_n}{b_n}=2\\ b_7=b_1\cdot q^6=4\cdot2^6=4\cdot64=256$

Answer 2

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. In this case, the geometric progression is defined by the following conditions:

- b1 = 4 - Bn+1 = 2bn

To find the value of b7, we can use the formula for the nth term of a geometric progression:

bn = b1 * r^(n-1)

where bn is the nth term, b1 is the first term, r is the common ratio, and n is the position of the term.

Finding b7

To find b7, we substitute the given values into the formula:

b7 = b1 * r^(7-1)

Substituting b1 = 4 and Bn+1 = 2bn, we have:

b7 = 4 * r^6

Now, we need to find the value of the common ratio, r. We can do this by using the given condition Bn+1 = 2bn:

Bn+1 = 2bn

Substituting n = 6, we have:

B7 = 2b6

Since B7 is the next term after b6, we can substitute B7 = 2b6 into the formula for bn:

2b6 = b1 * r^(6-1)

Substituting b1 = 4, we have:

2b6 = 4 * r^5

Now, we have two equations:

1. b7 = 4 * r^6 2. 2b6 = 4 * r^5

We can solve these equations simultaneously to find the value of r.