Respuesta :

gmany

Step-by-step explanation:

OK. It's an arithmetic sequence:

[tex]a_1=20,\ a_2=18.5,\ a_3=17,\ ...\\\\a_1=20,\ d=-1.5[/tex]

The explicit formula of an arithmetic sequence:

[tex]a_n=a_1+(n-1)d[/tex]

Substitute:

[tex]a_n=20+(n-1)(-1.5)=20-1.5n+1.5=21.5-1.5n[/tex]

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

[tex]\sum\limits_{n=1}^{10}(21.5-1.5n)[/tex]

What are your mistakes:

[tex]\sum\limits_{n=20}^{6.5}\to\boxed{n=20},\ \boxed{6.5}[/tex]

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

[tex]\sum\limits_{n=1}^{10} - \text{the sum for n = 1 to n = 10}[/tex]

znk

Answer:

[tex]\boxed{\displaystyle \sum_{k=1}^{10}(21.5 - 1.5n)}[/tex]

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

[tex]\displaystyle \sum_{k=1}^{n} a_{k}\\k \text{ is the index or counter}\\n \text{ is the number of the last term}\\a_{k} \text{ is the general formula for each term}[/tex]

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

[tex]\boxed{\displaystyle \sum_{k=1}^{10}(21.5 - 1.5n)}[/tex]

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