Question

(Bn) Bn=54. q=3. Sn=80две третьих найти B1-? n-?. ​

Answer 1

Відповідь: b1=2/3; n=5

Покрокове пояснення: фото

Answer 2

To find the first term (B1) and the total number of terms (n) in the arithmetic sequence (Bn), we have the following information:

Bn = 54 q = 3 (common difference) Sn = 80 (sum of the first n terms)

The formula for the sum of an arithmetic sequence is:

Sn = n/2 * (B1 + Bn)

Now, we are given Sn = 80 and we need to find B1 and n.

Step 1: Find n We know Sn = 80 and Bn = 54. Let's plug in these values and solve for n:

80 = n/2 * (B1 + 54)

Step 2: Find B1 Now that we have the value of n, we can use it to find B1. Let's rearrange the formula to solve for B1:

B1 = Sn * 2 / n - Bn

Now, let's plug in the values we have:

B1 = 80 * 2 / n - 54

Since we know n = 80/3, we can substitute it into the equation:

B1 = 80 * 2 / (80/3) - 54 B1 = 160 / (80/3) - 54 B1 = 160 * 3 / 80 - 54 B1 = 480 / 80 - 54 B1 = 6 - 54 B1 = -48

So, the first term (B1) is -48.

Now, to find n, we know:

n = 80/3 n ≈ 26.67

Since n must be a positive integer (we can't have a fraction of a term), we round up to the nearest whole number:

n = 27

Therefore, the total number of terms (n) in the arithmetic sequence is 27.