Question

Найти a1 и d a4=5.5 a23=34

Answer 1

Ответ: а1 = 1, d = 1,5

Объяснение:

an = a1 + d(n-1)

1) В формулу подставляем имеющиеся значения и решаем систему уравнений с двумя неизвестными:

5,5 = а1 + d (4 - 1)

34 = a1 + d (23 - 1)

упрощаем:

а1 + 3d = 5,5

а1 + 22d = 34

2) Вычтем из первого уравнение второе:

а1 + 3d - а1 - 22d = 5,5 - 34

-19d = -28,5

d = -28,5/(-19)

d =1,5

3) Подставим полученное d в первое уравнение:

а1 + 3*1.5 = 5,5

а1 = 5,5 - 3*1,5

а1 = 5,5 - 4,5

а1 = 1

Ответ: а1 = 1, d = 1,5

Answer 2

To find the values of the first term (a1) and the common difference (d) in an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * d

where: an = the nth term a1 = the first term d = the common difference n = the term number

Given that a4 = 5.5 and a23 = 34, we can use this information to set up two equations and then solve for a1 and d.

1. Using a4: a4 = a1 + (4 - 1) * d 5.5 = a1 + 3d

2. Using a23: a23 = a1 + (23 - 1) * d 34 = a1 + 22d

Now, we have a system of two equations with two variables (a1 and d). Let's solve this system:

Step 1: Subtract Equation 1 from Equation 2 to eliminate a1. (34) - (5.5) = (a1 + 22d) - (a1 + 3d) 28.5 = 19d

Step 2: Solve for d. d = 28.5 / 19 d = 1.5

Step 3: Substitute the value of d back into Equation 1 to solve for a1. 5.5 = a1 + 3 * 1.5 5.5 = a1 + 4.5

Step 4: Solve for a1. a1 = 5.5 - 4.5 a1 = 1

So, the first term (a1) is 1, and the common difference (d) is 1.5 in the arithmetic sequence.