Question

How to solve it using explicit formula

Answer 1

Answer:

Step-by-step explanation:

For these we always want to see how much each term is decreasing by, this will tell us what kind of series  it is.

-40, -47, -54, -61

Each time it DECREASES by -7, so it is an arithmetic sequence

The explicit form is found with two parts.  the start and how much each term changes by.  The start is -40 and the change is -7, so the explicit formula is -40 - 7(n-1).  This is assuming the first term is a_1.  If you are starting with a_0 instead you want to make (n-1) be n.  so if a_0 = -40 then you have -40 - 7n but if -40 = a_1 then you have -40 - 7(n-1)

the next one has a "common difference" of 30.  so now if -8 is a_0 you have -8 + 30n but if -8 is a_1 then you have -8 + 30(n-1)