Answer:
[tex]\sum_{a=1}^{7}(500-a)=3472[/tex]
Step-by-step explanation:
[tex]\sum_{a=1}^{7}(500-a)[/tex] will form a sequence as,
499, 498, 497.......7 terms
Since there is a common difference between successive and previous term,
d = 498 - 499 = -1
This sequence is an arithmetic sequence.
Sum of n terms of an arithmetic sequence is,
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
where a = first term of the sequence
n = number of term
d = common difference
For the given given sequence,
[tex]S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)][/tex]
= [tex]\frac{7}{2}[998-6][/tex]
= [tex]\frac{7}{2}(992)[/tex]
= 3472
Therefore, sum of seven terms of the given sequence will be 3472.
