Question

В арифметической прогрессии а7= -20, а17= -15. Найдите а20. Распишите подробно, пожалуйста!!!

Answer 1

D=(-15-(-20))/10=0,5
a7=a1+d6
a1=-20-6*0,5=-20-3=-23
a20=-23+0,5*19=-23+9,5=-13,5

Answer 2

Arithmetic Progression Problem

To find the value of a20 in the arithmetic progression where a7 = -20 and a17 = -15, we can use the formula for the nth term of an arithmetic progression:

a_n = a_1 + (n-1)d

Where: - a_n is the nth term - a_1 is the first term - n is the term number - d is the common difference

Calculating the Common Difference (d)

First, let's calculate the common difference (d) using the given terms a7 and a17.

We can use the formula: a_n = a_1 + (n-1)d

For a7: - a_7 = a_1 + 6d = -20 [[2 #]]

For a17: - a_17 = a_1 + 16d = -15 [[2 #]]

Subtracting the equation for a7 from the equation for a17: - a_17 - a_7 = 10d = 5 - d = 0.5

So, the common difference (d) is 0.5.

Finding a20

Now that we have the common difference, we can find a20 using the formula for the nth term of an arithmetic progression:

a_n = a_1 + (n-1)d

Substitute the values: - a_1 = a_7 - 6d = -20 - 6(0.5) = -23 - n = 20 - d = 0.5

Using the formula: a_20 = -23 + 19(0.5) = -23 + 9.5 = -13.5

So, the value of a20 in the given arithmetic progression is -13.5.