Algebra 2 and have 2 questions

Question

How can the series [ -6,+-3+0+3+6+9+12+15] be denoted using sigma notation?

Given the ordered pairs (1,5), (2,25), (3,125), what is an explicit (geometric) rule for this sequence?

Answer 1

1. Since the terms increase by 3, you could write ∑ 3n - 9, from n = 1 to 8 (write the limits under and above the sigma)
2. For (x,y), y = 5^x

To formally use the explicit rule in the format a_n = a₁r^n-1

write a_n = 5(5^n-1)