Find the sum of 997 + 992 + 987 +...+ 257 +252

  93,675

Step-by-step explanation:

We see that the given sequence is an arithmetic sequence with first term 997, common difference -5, and last term 252.

The number of terms in the sequence (n) can be found from the formula for the n-th term:

  an = a1 +d(n -1)

  (an -an)/d +1 = n

  (252 -997)/(-5) +1 = n = 150

The sum of these terms is the average of the first and last terms, multiplied by the number of terms:

  S150 = (997 +252)/2·150 = 93,675

The sequence sum is 93,675.