Respuesta :
The sum of the terms of the given sequence will be 648.
What is the arithmetic sequence?
An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value.
The given sequence is representing an arithmetic sequence.
Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6
3 - (-3) = 3 + 3 = 6
Since last term of the sequence is 81.
By the explicit formula of an arithmetic sequence, we can find the number of terms of this sequence.
[tex]\rm T_n= a+(n-1)d\\\\[/tex]
Where a = first term of the sequence, d = common difference.
Substitute all the values in the formula
[tex]\rm T_n= a+(n-1)d\\\\ 81 = -9 + 6(n - 1)\\\\ 81+9 =6(n-1)\\\\90=6(n-1)\\\\ n-1=\dfrac{90}{6}\\\\n-1=15\\\\n = 15+1\\\\n=16[/tex]
Now we know the sum of an arithmetic sequence is represented by
[tex]\rm S_{16}=\dfrac{16}{2}[-9+(16-1)6]\\\\S_{16}=8 [-9+15\times 6]\\\\S_{16}=8 [-9+90}\\\\S_{16} = 8 \times 81\\\\S_{16}=648[/tex]
Hence, the sum of the terms of the given sequence will be 648.
To know more about arithmetic sequence click the link given below.
https://brainly.com/question/4199153
