Two ways. By listing and adding and by formula.
19
+17
36
+15
51
+13
64
+11
75
+ 9
84
+ 7
91
Answer: 7 terms
By algebra:
This is an arithmetic series with first term = a1 = 19 and
common difference d=-2. We want the sum Sn to = 91, so we
substitute in
Sn = [2a1 + (n-1)d]
and solve for n
91 = [2(19) + (n-1)(-2)]
91 = [2(19) + (-2)(n-1)]
91 = [38 - 2(n-1)]
91 = [38 - 2n + 2]
91 = [40 - 2n]
91 = 20n - nē
nē - 20n + 91 = 0
(n-7)(n-13) = 0
n-7=0; n-13=0
n=7; n=13
Answers: 7 terms and 13 terms.
13 is another solution because sooner or later
the sequence starts adding negative numbers and the sum
starts coming back down and gets back to 91.
19
+17
36
+15
51
+13
64
+11
75
+ 9
84
+ 7
91
+ 5
96
+ 3
99
+ 1
100
-1
99
-3
96
-5
91
Edwin
