Question

-4; -2; 0 - арефмитическая прогрессия. Найти S10

Answer 1

S10=50.
Решение на фото в приложении.

Answer 2

To find the sum of the first 10 terms of an arithmetic progression, we can use the formula for the sum of an arithmetic progression:

Sₙ = (n/2) * (a₁ + aₙ),

where Sₙ is the sum of the first n terms, a₁ is the first term, aₙ is the nth term, and n is the number of terms.

In this case, we are given the first three terms of the arithmetic progression:

a₁ = -4 (first term) a₂ = -2 (second term) a₃ = 0 (third term)

We need to find a₉, which is the ninth term, since we want to find S₁₀ (the sum of the first 10 terms).

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

aₙ = a₁ + (n - 1) * d,

where d is the common difference between consecutive terms.

In our case, we can find d using the difference between any two consecutive terms:

d = a₂ - a₁ d = (-2) - (-4) d = 2.

Now, let's find a₉:

a₉ = a₁ + (9 - 1) * d a₉ = -4 + 8 a₉ = 4.

Now that we have a₁ and a₉, we can find S₁₀:

S₁₀ = (10/2) * (a₁ + a₉) S₁₀ = (10/2) * (-4 + 4) S₁₀ = 5 * 0 S₁₀ = 0.

Therefore, the sum of the first 10 terms of the arithmetic progression is 0.