How do you solve this arithmetic series problem given first term is 9 common difference is -3 sum of the terms is 0 then find the number of terms?

Answer 1

Te sequence is defined by

t(n) = 12 - 3n where n = 1, 2, 3, ...

The sum of the first k terms of this sequence is 12k - 3*k*(k+1)/2

Therefore 12k - 3k*(k+1)/2 = 0

12k = 3k*(k+1)/2

8 = k+1

so that k = 7

Answer 2

To solve this arithmetic series problem, you can use the formula: Sn = (n/2) * (2a + (n-1)d), where Sn is the sum of the series, a is the first term, d is the common difference, and n is the number of terms. Substituting the given values, we have: 0 = (n/2) * (2(9) + (n-1)(-3)). Simplifying, we get: 0 = (n/2) * (18 - 3n + 3). Rearranging and simplifying further, we have: 0 = 9n^2 - 27n. Factoring out n, we get: n(9n - 27) = 0. Therefore, either n = 0 or n = 3. Since the number of terms cannot be zero, the number of terms in the series is 3.