Question

What is the answer, what are the steps to solve this, and what do the parts of the equation represent?

Answer 1

Answer:

$\sum_{a=1}^{7}(500-a)=3472$

Step-by-step explanation:

$\sum_{a=1}^{7}(500-a)$ 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,

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

where a = first term of the sequence

n = number of term

d = common difference

For the given given sequence,

$S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)]$

    = $\frac{7}{2}[998-6]$

    = $\frac{7}{2}(992)$

    = 3472

Therefore, sum of seven terms of the given sequence will be 3472.