Given an arithmetic progression 17,13,9, find the number of terms required so that its sum is - 33 .

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

Simplify:

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

Then the last term is given by:

Substitute:

Solve for k:

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

answer: the answer is 35%