An arithmetic sequence has a first term of 0 and a 10th term of 15. If 10 is an output of the sequence, which term number is it? Show and explain how you know you have the correct answer.

Answer 1

the general term of an AS is
a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms

so :
a = 0
a+9d = 15
0+9d = 15
d = 15/9 = 5/3

For 10 to be one of the terms
a + (n-1)d = 10
0 + (n-1)(5/3) = 10
times 3:
5(n-1) = 30
5n-5 = 30
5n = 35
n = 7

check:
term(7) = a+6d
= 0 + 6(5/3) = 10
All is good!