Respuesta :

Answer:

[tex]S_{40}=6560[/tex]

Step-by-step explanation:

Given the sequence

[tex]4,12,20,28,\cdots[/tex]

We know that:

The first term, a=4

Also, 21-4=20-12=28-20=8

Therefore, the sequence is an arithmetic sequence with:

Common difference, d=8

For an arithmetic sequence, the sum

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d] \\$Therefore$:\\\\S_{40}=\dfrac{40}{2}[2(4)+(40-1)*8] \\=20(8+39*8)\\=20(8+312)\\=20*320\\=6560[/tex]

The sum of the first 40 terms is 6560.