<span> To get an explicit formula, we need to find an expression which gives the n-th term without having to compute earlier terms in the sequence. Looking at the numbers, and from the recursive formula, we see that the sequence is built by subtracting n from the previous term. This is similar to the triangular number sequence 1,3,6,10,15,... which has the explicit formula a_n = n(n+1)/2. In our case we are subtracting n from the previous term, so we multiply by -1/2 instead of 1/2. However, we also need to add a constant term to reproduce the numbers of the sequence. We can write a_1 = -1(2)/2 + c = 8. Therefore, c = 9.
So the explict formula is:
a_n = -n(n+1)/2 + 9</span>
-11 ≤ 6 - 2n - 5
-11 ≤ -2n + 1
-11 (-1) ≤ -2n + 1 (-1)
-12 ≤ -2n
-12/-2 ≤ -2n/-2
6 ≥ n
(remember, you only flip the sign if you are <em>dividing </em>a negative number
6 ≥ n is your answer
hope this helps
Answer:
D, -42 multiply 6 on both sides