Hello! My teacher gave me this study guide on sequence, and I'm having a bit trouble with a few problems, could someone please help me out and explain?

Question

1. Find the sum −3 + 4 + 11 + ⋯ + 67
2. Find the sum 2 + 10 + 50 + ⋯ + 2 ∙ 5¹³
3. Write out the first three terms and the final term. Then find the sum. :

30

∑ (3k-4)

k=0

4. Write the sum using ∑ notation and find the sum: 3 + 9 +15 + . . . + 549

Thank you!

Answer 1

You do not have sequences, you have series!

The arithmetic series has sum (n/2)(a₁+a_n)

The geometric series has sum (a-arⁿ⁺¹)/(1-r).

The sum of n integers is n(n+1)/2.