Question

Дана арифметическая прогрессия (Аn) у которой а 4 =4,d=-3. Найти: а8, а9, а23, а11, а15, а27 помогите пожалуйста.

Answer 1

An=A1+d(n-1) A1=An-d(n-1) A1=4+9 A1=13 A8=13+(-3*7) A8=-8 a9=13+(-3*8) A9=-11 A11=13+(-3*10) A11=-17 A15=13+(-3*14) A15=-29 A23=13+(-3*22) A23=-53 A27=13+(-3*26) A27=-65

Answer 2

Arithmetic Progression (Аn)

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, we are given an arithmetic progression with a fourth term (a4) equal to 4 and a common difference (d) of -3.

To find the eighth term (a8), we can use the formula for the nth term of an arithmetic progression:

an = a1 + (n - 1) * d

where: - an is the nth term - a1 is the first term - n is the position of the term in the sequence - d is the common difference

Calculating a8

Using the given information, we can substitute the values into the formula:

a8 = a1 + (8 - 1) * d

Since a4 is the fourth term, we can find a1 by subtracting 3 times the common difference from a4:

a1 = a4 - 3d

Substituting the values, we get:

a1 = 4 - 3 * (-3) = 4 + 9 = 13

Now we can calculate a8:

a8 = 13 + (8 - 1) * (-3) = 13 + 7 * (-3) = 13 - 21 = -8

Therefore, the eighth term (a8) of the arithmetic progression is -8.

Calculating a9

To find the ninth term (a9), we can use the same formula:

a9 = a1 + (9 - 1) * d

Substituting the values, we get:

a9 = 13 + (9 - 1) * (-3) = 13 + 8 * (-3) = 13 - 24 = -11

Therefore, the ninth term (a9) of the arithmetic progression is -11.

Calculating a23

To find the twenty-third term (a23), we can again use the formula:

a23 = a1 + (23 - 1) * d

Substituting the values, we get:

a23 = 13 + (23 - 1) * (-3) = 13 + 22 * (-3) = 13 - 66 = -53

Therefore, the twenty-third term (a23) of the arithmetic progression is -53.

Calculating a11

To find the eleventh term (a11), we can use the formula:

a11 = a1 + (11 - 1) * d

Substituting the values, we get:

a11 = 13 + (11 - 1) * (-3) = 13 + 10 * (-3) = 13 - 30 = -17

Therefore, the eleventh term (a11) of the arithmetic progression is -17.

Calculating a15

To find the fifteenth term (a15), we can use the formula:

a15 = a1 + (15 - 1) * d

Substituting the values, we get:

a15 = 13 + (15 - 1) * (-3) = 13 + 14 * (-3) = 13 - 42 = -29

Therefore, the fifteenth term (a15) of the arithmetic progression is -29.

Calculating a27

To find the twenty-seventh term (a27), we can use the formula:

a27 = a1 + (27 - 1) * d

Substituting the values, we get:

a27 = 13 + (27 - 1) * (-3) = 13 + 26 * (-3) = 13 - 78 = -65

Therefore, the twenty-seventh term (a27) of the arithmetic progression is -65.

I hope this helps! Let me know if you have any further questions.