How do you solve this sequence/series problem?

Question

Given the first term and the common difference of an arithmetic sequence to find the explicit formula and the three terms in the sequence after the last one given

a₁=-34 d=-2

Answer 1

Hi there! I would love to help you out.

The explicit formula for an arithmetic sequence is:

a_n = a₁ + d(n-1) where a₁ is your first term, d is your difference, and n is the number of terms.

We can plug in the given information into the formula now:

a_n = -34 + -2(n - 1)

To find the first three terms we can do one of two things. Either plug in 2, 3, and 4 (we don't plug in 1 because a₁ is already given) in for n and record the results or we can just add our difference to the first term given:

a₂ = -34 + -2(2-1) = -36

a₃ = - 34 + -2(3-1) = -38

a₄ = -34 + -2(4-1) = -40

There you have it! I hope this explanation was thorough and answered all of your questions. If you have any additional questions please don't hesitate to reach out! Learn on! :)