arithmetic sequences

Letting a₁ be the first term, we have  that

[ a₁  + d(5-1)]   + [a₁ + d(10-1)]  = 11.5     simplify

2a₁ + 4d + 9d   =  11.5

2a₁ + 13d  = 11.5     →   2a₁  = 11.5 - 13d   (1)

And the sum of the first 20 terms can be expressed by :

85 = (20/2) [ 2a₁ + (20-1)d ]

85 = 10 [2a₁ + 19d]   (2)

Substituting (1)  into (2), we have

85 = 10 [ 11.5 - 13d + 19d]

85  = 115 + 60d

-30  = 60d     divide both sides by 60

-1/2  = d

And using (1)  to find the first term , a₁, we have

2a₁ = 11.5 - 13(-1/2)

2a₁  = 11.5 + 6.5

2a₁  = 18

a₁  = 9

9, 8.5, 8, 7.5, 7......................10th term=4.5,

So how did you get: 7(5th term) + 4.5(10th term)=11???????

Guest....read closely.......the sum of those two terms  = 11.5