The tenth erm of an arithematic sequence is 65 and its 15 th term is 80 .Is 200 a term of this sequence

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