The sum of the first six terms of an arithmetic sequence is 93 and the sum of the first two terms is 430. Find: ?
a. the sum of the first n terms
b. the smallest value of n for the sum to exceed 1000
a. the sum of the first n terms
b. the smallest value of n for the sum to exceed 1000
1 Answer
See below.
Explanation:
A generic arithmetic sequence is formed by terms like
Now, the sum of the first
The first equation of the system is thus
We also know about the sum of the first two terms, namely
Put the two together, and you have
NOTE: are you sure this is not a typo? I tried to solve the same equation, but with
So I'm assuming this is the correct one.
Now, the sum of the first
Also, since