Problema Solution
What is the sum of a 12–term arithmetic sequence where the last term is 13 and the common difference is –10?
Answer provided by our tutors
First we will find all of the terms using the general equation a_n=a_1+(n-1)*d)
12th term
13
1st term
13=a_1+(12-1)(-10)
a_1=123
2nd term
a_2=123+(2-1)(-10)
a_2=113
and so on to get:
3rd term: 103
4th term: 93
5th term: 83
6th term: 73
7th term: 63
8th term: 53
9th term: 43
10th term: 33
11th term: 23
Now we can add them all up to get the sum:
123+113+103+93+83+73+63+53+43+33+23+13=816