Question
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.
Answers
Reiny
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!
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!