Question

Найти сумму 21 членов арифметичной прогрессии An a1=-3, a20=-7 пожалуйста помогите

Answer 1

A2 = a1 + d
-3 = 3 + d
d = -6

a20 = a1 + 19d = 3 - 6*19 = -111

S20 = (a1 + a20)*20/2 = (3 - 111) * 10 = -108 * 10 = -1080

Ответ: -1080

Answer 2

Finding the Sum of 21 Terms in an Arithmetic Progression

To find the sum of 21 terms in an arithmetic progression with given first and twentieth terms, we can use the formula for the sum of an arithmetic series:

Sum of n terms (S_n): S_n = n/2 * (a₁ + a_n)

Where: - n = number of terms - a₁ = first term - a_n = nth term

Given: - a₁ = -3 - a₂₀ = -7 - n = 21

Calculation

Using the given values, we can calculate the sum of the 21 terms in the arithmetic progression:

a₁ = -3 a₂₀ = -7 n = 21

First, we need to find the common difference (d) using the given terms: d = (a₂₀ - a₁) / (20 - 1) d = (-7 - (-3)) / (20 - 1) d = (-7 + 3) / 19 d = -4 / 19

Now, we can find the 21st term (a₂₁): a₂₁ = a₁ + (n - 1) * d a₂₁ = -3 + (21 - 1) * (-4 / 19) a₂₁ = -3 + 20 * (-4 / 19) a₂₁ = -3 + (-80 / 19) a₂₁ = (-57 / 19)

Finally, we can calculate the sum of the 21 terms (S₂₁): S₂₁ = 21/2 * (-3 + (-57 / 19)) S₂₁ = 21/2 * (-3 - 57/19) S₂₁ = 21/2 * (-57/19 - 57/19) S₂₁ = 21/2 * (-114/19) S₂₁ = -1071/38

Therefore, the sum of the 21 terms in the arithmetic progression is -1071/38.