Question

Дано: a1= - 8, n=17, Sn=- 408. Найдите разность арифметической прогресии (An)​

Answer 1

Используем формулу:

$S_n=\dfrac{2a_1+d(n-1)}{2}\cdot n$

После подстановки известных данных получим:

$-408=\dfrac{2\cdot(-8)+16d}{2}\cdot 17$

$\dfrac{-16+16d}{2}\cdot 17=-408$

$\dfrac{16d-16}{2}=-24$

$8d-8=-24$

$8d=-16$

$d=-2$

Ответ: -2

Answer 2

Arithmetic Progression (AP) Formula

To find the difference of an arithmetic progression (AP), we can use the formula:

An = a1 + (n-1)d

Where: - An is the nth term of the AP - a1 is the first term of the AP - n is the number of terms in the AP - d is the common difference between consecutive terms

In this case, we are given: - a1 = -8 - n = 17 - Sn = -408 (the sum of the AP)

To find the difference (d), we need to rearrange the formula to solve for d:

d = (Sn - a1) / (n - 1)

Substituting the given values:

d = (-408 - (-8)) / (17 - 1)

Simplifying the equation:

d = (-408 + 8) / 16

d = -400 / 16

d = -25

Therefore, the difference of the arithmetic progression is -25.