Question

А5=0,2а16= - 7,5Найти а1, d

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To find the values of a1 and d, we'll first use the formulas for the nth term of an arithmetic sequence to express a5 and a16 in terms of a1 and d. Then, we'll use the given values of a5 and a16 to solve for a1 and d.

In an arithmetic sequence, the nth term is given by:

an = a1 + (n - 1) * d

where: an = the nth term of the sequence a1 = the first term of the sequence d = the common difference between consecutive terms n = the position of the term in the sequence

Given: a5 = 0.2 a16 = -7.5

Let's start by finding the expressions for a5 and a16:

1. For a5: a5 = a1 + (5 - 1) * d 0.2 = a1 + 4d ...........(Equation 1)

2. For a16: a16 = a1 + (16 - 1) * d -7.5 = a1 + 15d ..........(Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (a1 and d). Let's solve this system of equations.

Step 1: Multiply Equation 1 by 15 and Equation 2 by 4 to eliminate the variable d:

(15) * (0.2 = a1 + 4d) 3 = 15a1 + 60d ...........(Equation 3)

(4) * (-7.5 = a1 + 15d) -30 = 4a1 + 60d ..........(Equation 4)

Step 2: Now, subtract Equation 4 from Equation 3 to eliminate the variable d:

(3) - (-30) = (15a1 + 60d) - (4a1 + 60d) 33 = 15a1 - 4a1 33 = 11a1

Step 3: Solve for a1:

a1 = 33 / 11 a1 = 3

Step 4: Substitute the value of a1 (which is 3) into Equation 1 to find d:

0.2 = a1 + 4d 0.2 = 3 + 4d

Step 5: Solve for d:

4d = 0.2 - 3 4d = -2.8

d = -2.8 / 4 d = -0.7

So, the values of a1 and d are: a1 = 3 d = -0.7