Question

1) B1 = -4, q = -3, Sn = 728. Найти: n 2) b3 = 18, b5 = 450, q < 0. Найти: S4 С Решением

Answer 1

Ответ:

решение смотри на фотографии

Объяснение:

Answer 2

To solve both problems, we can use the formulas for the sum of an arithmetic sequence and the nth term of an arithmetic sequence.

1. For the first problem: Given: B1 = -4, q = -3, Sn = 728

The sum of an arithmetic sequence (Sn) can be calculated using the formula: Sn = (n/2) * (B1 + Bn)

Also, the nth term of an arithmetic sequence (Bn) can be calculated using the formula: Bn = B1 + (n - 1) * q

Let's solve for n:

We know B1 = -4, q = -3, and Sn = 728. We need to find n.

Using the formula for Bn: Bn = -4 + (n - 1) * (-3)

Now, we can use the formula for Sn: Sn = (n/2) * (B1 + Bn)

Substitute the values we know: 728 = (n/2) * (-4 + (-4 + (n - 1) * (-3)))

Simplify the equation: 728 = (n/2) * (-8 - 3n)

Multiply both sides by 2 to eliminate the fraction: 1456 = n * (-8 - 3n)

Expand the right side: 1456 = -8n - 3n^2

Rearrange the equation to form a quadratic equation: 3n^2 + 8n - 1456 = 0

Now we can solve this quadratic equation. You can use the quadratic formula or factorization to find the values of n. The solutions for n will be two integers. Once you find the values of n, you can verify them by calculating the sum (Sn) to ensure it equals 728.

2. For the second problem: Given: b3 = 18, b5 = 450, q < 0

We are asked to find S4, which is the sum of the first 4 terms of the arithmetic sequence.

The nth term of an arithmetic sequence (Bn) can be calculated using the formula: Bn = B1 + (n - 1) * q

Given that q < 0, we know that the common difference (q) is negative.

We are given b3 = 18, which means B3 is the third term of the sequence: B3 = b1 + (3 - 1) * q 18 = b1 + 2q

We are also given b5 = 450, which means B5 is the fifth term of the sequence: B5 = b1 + (5 - 1) * q 450 = b1 + 4q

Now we have two equations:

1. 18 = b1 + 2q
2. 450 = b1 + 4q

We can solve these equations simultaneously to find the values of b1 and q. Once we have b1 and q, we can find the fourth term (B4) using the formula for the nth term. Finally, we can find S4, the sum of the first 4 terms, using the formula for the sum of an arithmetic sequence:

S4 = (4/2) * (b1 + B4)

Solve for b1 and q, find B4, and then calculate S4 using the above formula.