Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + + 67

summation of the quantity negative eight plus five n from n equals zero to fifteen

summation of negative forty times n from n equals zero to infinity

summation of negative forty times n from n equals zero to fifteen

summation of the quantity negative eight plus five n from n equals zero to infinity

-8 - 3 + 2 + 7 + ... + 67     hmm... so the first term's value is -8.  If you notice, it went from -8, to -3 and then +2 and so on.... you can always get the "common difference" d by simply getting the difference of two terms, so d = +2 -(- 3)  ----> d = +2+3  ----> d = 5.

now.. the last value is 67.. but what term is that anyway?

well, let's use the arithmetic sequence equation to see who that is.



so, is the 16th term  alrite.. .hmmm, so it begins with -8, then keeps on adding 5 16 times



both forms are the same, so.. hmm it depends on how simplified you need it.