Final answer:
The sum 89+84+79+74+.... +9+4 can be written in sigma notation as Σ from i=1 to 18 of (94 - 5i), after determining the sequence is arithmetic with a common difference of -5 and 18 terms total.
Step-by-step explanation:
To write the sum 89+84+79+74+.... +9+4 in sigma notation, we first observe the pattern of the sequence. We notice that each term is 5 less than the previous term, indicating we're dealing with an arithmetic sequence. The first term, a1, is 89, and the common difference, d, is -5. The last term of the sequence is 4, but we need to determine how many terms there are in the sequence. We can use the formula for the nth term of an arithmetic sequence, which is an = a1 + ( n - 1) * d.
Let's find n such that 4 = 89 + ( n - 1)(-5). Solving for n, we get n = 18. Now we can write the sum in sigma notation:
Σi=118 (94 - 5i)