Question

An- арифм прогрессия a1=-8 d=2 найти a20 s10

Answer 1

Ответ:

30,10

Объяснение:

a20=a1+d(n-1)

a20=-8+2(20-1)=30

S10=((2a1+d(n-1))*n)/2

S10=(2*(-8)+2*(10-1))*10/2=10

Answer 2

To find the 20th term (a20) and the sum of the first 10 terms (S10) of the arithmetic progression with the given first term (a1) and common difference (d), we can use the formulas for these calculations.

The nth term (an) of an arithmetic progression is given by the formula: an = a1 + (n - 1) * d

The sum of the first n terms (Sn) of an arithmetic progression is given by the formula: Sn = (n / 2) * (a1 + an)

Given: a1 = -8 (the first term) d = 2 (the common difference)

Let's first find a20:

a20 = a1 + (20 - 1) * d a20 = -8 + (20 - 1) * 2 a20 = -8 + 19 * 2 a20 = -8 + 38 a20 = 30

Now, let's find S10:

S10 = (10 / 2) * (a1 + a10) S10 = 5 * (a1 + a10)

To find a10, we can use the same formula for finding the nth term:

a10 = a1 + (10 - 1) * d a10 = -8 + (10 - 1) * 2 a10 = -8 + 9 * 2 a10 = -8 + 18 a10 = 10

Now, we can calculate S10:

S10 = 5 * (a1 + a10) S10 = 5 * (-8 + 10) S10 = 5 * 2 S10 = 10

So, the 20th term (a20) is 30, and the sum of the first 10 terms (S10) is 10.