Is this correct? the writing in red is all my work. it's about sigma notation.

Step-by-step explanation:

OK. It's an arithmetic sequence:

The explicit formula of an arithmetic sequence:

Substitute:

The sigma notation of the sum of the first ten terms:

What are your mistakes:

The first ten terms, not from 20th to 29th (you wrote 6.5?)

Step-by-step explanation:

If you have an arithmetic sequence

a₁ + a₂ + a₃ + … + aₙ

the general sigma notation for the sum of the first n terms is

k = 1 means that you start at the first term and keep incrementing until k = n.

The formula for the nth term of an arithmetic sequence is

aₙ = a₁ + (n - 1)d

In your sequence,

a₁ = 20 and d= -1.5, so

aₙ = 20 - 1.5(n - 1) =20 - 1.5n + 1.5 = 21.5 - 1.5n

Thus, the sigma notation for your sequence is

i'm not sure i quite understand, could you provide more information?