Question

Найти сумму первых 10 членов арифметической прогрессии -23;-20;...

Answer 1

D=a_2-a_1=-20-(-23)=3
S_n=((2a_1 + (n-1)d)/2) × n
S_10=((2×(-20)+9×3)/2)×10=-65

Answer 2

Calculating the Sum of the First 10 Terms of an Arithmetic Progression

To find the sum of the first 10 terms of the arithmetic progression with the given terms (-23, -20, ...), we can use the formula for the sum of an arithmetic progression.

The formula for the sum of the first n terms of an arithmetic progression is given by: S(n) = (n/2) * (a(1) + a(n))

Where: - S(n) is the sum of the first n terms - n is the number of terms - a(1) is the first term - a(n) is the nth term

Applying the Formula

Using the given terms: - First term, a(1) = -23 - Tenth term, a(10) = -20 + (10-1)d = -20 + 9d

The common difference, d, can be calculated using the formula: d = a(2) - a(1)

Calculating the Common Difference

From the given information: - Second term, a(2) = -20

Using the formula: d = a(2) - a(1) = -20 - (-23) = 3

So, the common difference d is 3.

Calculating the Sum

Now, we can calculate the sum of the first 10 terms using the formula: S(10) = (10/2) * (-23 + (-20 + 9d))

Substituting the value of d: S(10) = 5 * (-23 + (-20 + 9*3))

Solving the expression: S(10) = 5 * (-23 + (-20 + 27)) = 5 * (-23 + 7) = 5 * (-16) = -80

Therefore, the sum of the first 10 terms of the given arithmetic progression is -80.