In this particular arithmetic sequence, a6 = 36 and a17 = 113. What is the value of a23?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.
A. a23 = 101
B. a23 = 155
C. a23 = 162
D. a23 = 167
+130518 36 = a1 + d ( 6 -1) → 36 = a1 + 5d (1)
113 = a1 + d ( 17 -1) → 113 = a1 + 16d (2)
Subtract (1) from (2)
77 = 11d divide both sides by 11
7 = d
And using (1) to find a1, we have
36 = a1+ 5(7)
36 = a1 + 35 so........a1 must = 1
And
a23 = 1 + 7(23 -1)
a23 = 1 + 7(22)
a23 = 155
