Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 29. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?  Choose the correct choice from the following options.
A) 1  B) 13  C) 15  D) 21  E) 47
We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.   What does this imply?If the sum of the first n terms of the sequence is n   Since number of terms will definitely be positive, we are looking for a positive sum.   19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on   Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...   Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.   Answer (21)
<result>D</result>
Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 29. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?