Question

Найдите суму восьми первых членов арифметической прогресии ,если А1=5, а А5=(-7) СРОЧНО!!!!!!!

Answer 1

Sn = (a1 + an)/2 * n; an = a1 + d*(n - 1)

S8 = (a1 + a8)/2 * 8 = 4*(a1 + a8) = 4*(2a1 + 7d)

a1 = 5

a5 = a1 + 4d

a1 + 4d = -7

5 + 4d = -7

4d = -12

d = -3

S8 = 4*(2*5 + 7*(-3)) = 4*(10 - 21) = 4*(-11) = -44

Answer 2

Calculation of the Sum of the First Eight Terms of an Arithmetic Progression

To find the sum of the first eight terms of an arithmetic progression, we need to know the first term (A1) and the common difference (d). In this case, we are given that A1 = 5 and A5 = -7.

To calculate the sum, we can use the formula for the sum of an arithmetic progression:

Sn = (n/2)(2A1 + (n-1)d)

where Sn is the sum of the first n terms, A1 is the first term, and d is the common difference.

In this case, we want to find the sum of the first eight terms, so n = 8.

Let's substitute the given values into the formula:

S8 = (8/2)(2(5) + (8-1)(-7))

Simplifying the equation:

S8 = 4(10 + 7(-7))

S8 = 4(10 - 49)

S8 = 4(-39)

S8 = -156

Therefore, the sum of the first eight terms of the arithmetic progression is -156.