Question

Выписано несколько последовательных членов арифметической прогрессии -8;-2;2;6. Найдите сумму 11 первых членов этой прогрессии

Answer 1

РЕШЕНИЕ
a1 = - 6
a2 = - 2
Разность прогрессии
d = a2 - a1 = -2 - (-6) = 4.
а11 = а1 + 10*d = - 6 + 40 = 34 
Сумма n = 11 членов.
S(n) = (a1 + an)* n/2 = (-6 + 34)*5.5 = 28 * 5*5 = 154 - ОТВЕТ

Answer 2

Arithmetic Progression and Sum of Terms

To find the sum of the first 11 terms of the arithmetic progression -8, -2, 2, 6, we can use the formula for the sum of the first n terms of an arithmetic progression:

Sum of n terms = n/2 * (first term + last term)

First, let's find the common difference (d) of the given arithmetic progression: - Common difference (d) = 2nd term - 1st term = -2 - (-8) = 6

Now, we can find the sum of the first 11 terms using the formula: - Sum of 11 terms = 11/2 * (-8 + (11-1)*6)

Calculating the sum: - Sum of 11 terms = 11/2 * (-8 + 10*6) = 11/2 * (-8 + 60) = 11/2 * 52 = 286

So, the sum of the first 11 terms of the given arithmetic progression is 286.