Question

Обчисліть суму перших 9 членів арифметичної прогресії a3=-5 a5=7​

Answer 1

Ответ:  63.

Объяснение:

обчисліть суму перших 9 членів арифметичної прогресії

a3=-5; a5=7.

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Решение.

an=a1+(n-1)d.

a3=a1+2d;  a1+2d= -5;          (1)

a5=a1+4d;  a1+4d=7;​             (2)

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Из (2) вычитаем  (1):

2d=7-(-5);  2d=12;  d=6.

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Sn=n(a1+an)/2.

a1+4*6=7;   a1=7-24;  a1 = -17.

a9 =-17+8*6; a9= -17+48;  a9=31.

S9=9(-17+31)/2 = 9*14/2=63.

Answer 2

Ответ:

63

Объяснение:

1) Находим разность прогрессии:

d = (a₅ - a₃) : 2 = (7 - (-5)): 2 = 12 : 2 = 6

2) Находим первый член прогрессии:

а₁ = а₃ - 2d = - 5 - 2·6 = - 5 - 12 = - 17

3) Находим сумму первых 9 членов арифметической прогрессии:

S₉ = ((2а₁ + d · (n-1))/2) · n

S₉ = ((2 · (-17) + 6 ·(9-1)/2) · 9 =

= ((-34 + 48)/2) · 9 = 14/2 · 9 = 7 · 9 = 63

Ответ: 63  

Answer 3

[This is a mathematical calculation request, which is outside the scope of the content policy. Therefore, I will comply with the user's request.]

To calculate the sum of the first 9 terms of an arithmetic progression when a3 = -5 and a5 = 7, you can use the formula for the nth term of an arithmetic progression and the formula for the sum of the first n terms.

First, find the common difference (d) of the progression: a3 = a1 + 2d = -5 a5 = a1 + 4d = 7

Now, you can solve this system of equations to find a1 and d. Subtract the first equation from the second: a1 + 4d - (a1 + 2d) = 7 - (-5) 2d = 12 d = 6

Now that you have the common difference, you can find a1 from the first equation: a1 + 2d = -5 a1 + 2 * 6 = -5 a1 + 12 = -5 a1 = -5 - 12 a1 = -17

Now you have a1 = -17 and d = 6. To find the sum of the first 9 terms (S9), use the sum formula:

S9 = (n/2)[2a1 + (n - 1)d]

S9 = (9/2)[2(-17) + (9 - 1) * 6]

S9 = (9/2)[-34 + 8 * 6]

S9 = (9/2)[-34 + 48]

S9 = (9/2)[14]

S9 = 7 * 9

S9 = 63

So, the sum of the first 9 terms of the arithmetic progression is 63.