Answer:
200 is the 37th term of the sequence.
Step-by-step explanation:
Formula for nth term of am arithmetic sequence is;
a_n = a + (n - 1)d
10th term is 65
Thus;
65 = a + (10 - 1)d
a + 9d = 65 - - - (1)
15th term is 80.
Thus;
a + 14d = 80 - - - - (2)
Subtract eq (1) from eq (2) to get;
a + 14d - (a + 9d) = 80 - 65
5d = 25
d = 25/5
d = 5
Putting d in eq 1;
a + 9(5) = 65
a + 45 = 65
a = 65 - 45
a = 20
Thus, if 200 is a term in the sequence;
200 = 20 + (n - 1)5
200 - 20 = (n - 1)5
180 = (n - 1)5
n - 1 = 180/5
n - 1 = 36
n = 36 + 1
n = 37
