Question

Выписаны несколько членов арифметической прогрессии: -1;2;5 и т.д Найдите сумму первых пяти ее членов. Если можно,то с обьяснением

Answer 1

Ответ:

25

Пошаговое объяснение:

a₁=-1  a₂=2  a₃=5

S₅=(a₁+a₅)·5/2

a₅=a₁+d(5-1)

d=a₂-a₁=a₃-a₂  d=2-(-1)=3

a₅=-1+3·4=11

S₅=(-1+11)·5/2=25

Answer 2

Finding the Sum of the First Five Terms of an Arithmetic Progression

To find the sum of the first five terms of an arithmetic progression, we need to determine the common difference and the first term of the progression.

In this case, the given arithmetic progression is: -1, 2, 5, and so on.

To find the common difference, we subtract the second term from the first term: 2 - (-1) = 3.

Therefore, the common difference is 3.

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

nth term = first term + (n - 1) * common difference

Using the first two terms of the progression, we can substitute the values into the formula:

-1 = first term + (1 - 1) * 3

Simplifying the equation, we have:

-1 = first term

Therefore, the first term of the arithmetic progression is -1.

Now that we have the common difference (3) and the first term (-1), we can find the sum of the first five terms using the formula for the sum of an arithmetic progression:

Sum of n terms = (n/2) * (2 * first term + (n - 1) * common difference)

Substituting the values into the formula, we have:

Sum of 5 terms = (5/2) * (2 * (-1) + (5 - 1) * 3)

Simplifying the equation, we get:

Sum of 5 terms = (5/2) * (-2 + 4 * 3)

Sum of 5 terms = (5/2) * (-2 + 12)

Sum of 5 terms = (5/2) * 10

Sum of 5 terms = 25

Therefore, the sum of the first five terms of the given arithmetic progression is 25.