Answer:
Sum of the sequence will be 648
Step-by-step explanation:
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
Therefore, by the explicit formula of an arithmetic sequence we can find the number of terms of this sequence
[tex]T_{n}=a+(n-1)d[/tex]
where a = first term of the sequence
d = common difference
n = number of terms
81 = -9 + 6(n - 1)
81 + 9 = 6(n - 1)
n - 1 = [tex]\frac{90}{6}=15[/tex]
n = 15 + 1 = 16
Now we know sum of an arithmetic sequence is represented by
[tex]\sum_{n=1}^{n}(a_{n})=\frac{n}{2}(a_{1}+a_{n})[/tex]
Now we have to find the sum of the given sequence
[tex]S_{16}=\frac{16}{2}[-9 + (16-1)6][/tex]
= 8[-9 + 90]
= 8×81
= 648
Therefore, sum of the terms of the given sequence will be 648.
