Question

A1=-10,5; a10=12 ; S10-?

Answer 1

Смори 
а10=а1+9d
12=-10.5+9d
12+10.5=9d
22,5÷9=d
2.5=d
теперь 
1)а2=a1+d
  а2 =-8
2)а3=-5.5
3)а4=-3
4)а5=-0.5
5)а6=2
6)а7=4.5
7)а8=7
8)а9=9.5
9) сумма 10 членов прогресии = 12-10.5-8-5.5-3-0.5+2+4.5+7+9.5=7.5
ответ: 7.5

Answer 2

To find the sum of the first 10 terms of an arithmetic sequence, we can use the formula:

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

Where: Sn is the sum of the first n terms n is the number of terms a1 is the first term d is the common difference

In this case, we are given: a1 = -10.5 (the first term) a10 = 12 (the 10th term)

We can use this information to find the common difference, d.

a10 = a1 + (10-1)d 12 = -10.5 + 9d 22.5 = 9d d = 22.5 / 9 d = 2.5

Now, we can substitute the values into the sum formula to find the sum of the first 10 terms (S10):

S10 = (10/2) * (2(-10.5) + (10-1)(2.5)) S10 = 5 * (-21 + 9(2.5)) S10 = 5 * (-21 + 22.5) S10 = 5 * 1.5 S10 = 7.5

Therefore, the sum of the first 10 terms (S10) in the given arithmetic sequence is 7.5.