Question

Найти шестой член и разность арифметической прогрессии,если сумма ее пятого и седьмого членов равно 18,а второй член равен -3. Помогите пожалуйста))

Answer 1

18/2=9 - шестой член прогрессии.

 Возьмём x за  разность прогрессии получим:

3+4*x=9

x=(9-3)

4=6/4=1,5

Answer 2

Finding the Sixth Term and Common Difference of an Arithmetic Progression

To find the sixth term and the common difference of an arithmetic progression, we can use the given information about the sum of the fifth and seventh terms, as well as the value of the second term.

Given: - Sum of the fifth and seventh terms = 18 - Second term = -3

Calculating the Common Difference (q)

The formula for the sum of the first n terms of an arithmetic progression is given by: \[ S_n = \frac{n}{2} \times (a_1 + a_n) \]

Where: - \( S_n \) = sum of the first n terms - \( n \) = number of terms - \( a_1 \) = first term - \( a_n \) = nth term

Using the given information, we can calculate the common difference (q) using the formula: \[ S_n = \frac{n}{2} \times (a_1 + a_n) \] \[ 18 = \frac{2}{2} \times (-3 + a_7) \] \[ 18 = -3 + a_7 \] \[ a_7 = 21 \]

Now that we have the value of the seventh term, we can calculate the common difference (q) using the formula for the nth term of an arithmetic progression: \[ a_n = a_1 + (n-1)q \]

Using the given second term \( a_2 = -3 \), we can solve for the common difference (q): \[ -3 = a_1 + (2-1)q \] \[ -3 = a_1 + q \]

Calculating the Sixth Term (a_6)

Now that we have the common difference (q), we can calculate the sixth term (a_6) using the formula for the nth term of an arithmetic progression: \[ a_6 = a_1 + (6-1)q \]

Substituting the value of the second term (-3) and the common difference (q), we get: \[ a_6 = -3 + 5q \]

Using the calculated value of q, we can find the value of the sixth term.

Calculations: - \( a_7 = 21 \)- \( q = 3 \)- \( a_6 = -3 + 5q = -3 + 5*3 = 12 \)

Results

- The common difference (q) of the arithmetic progression is 3. - The sixth term of the arithmetic progression is 12.