Question

write the sum using summation notation, assuming the suggested pattern continues.
2-6+18-54+...

Answer 1

Each term seems like it's -3 times the previous one, first term 2.

$\displaystyle \sum_{k=0}^{\infty} 2 (-3)^k$

Going to infinity like that it's of course divergent, but perfectly summable if we replace infinity with a finite bound like n-1:

$\displaystyle \sum_{k=0}^{n-1} 2 (-3)^k$

But, assuming the pattern continues means I'd go with infinity.

Answer: $\displaystyle \sum_{k=0}^{\infty} 2 (-3)^k$