SOLUTION: Hi, I'm having a really tough time with these two questions. Any help is greatly appreciated, thank you! 1. For the sequence 15,12,9,... find the common difference and the nth t

Algebra ->  Sequences-and-series -> SOLUTION: Hi, I'm having a really tough time with these two questions. Any help is greatly appreciated, thank you! 1. For the sequence 15,12,9,... find the common difference and the nth t      Log On


   

Question 438685: Hi, I'm having a really tough time with these two questions. Any help is greatly appreciated, thank you!
1. For the sequence 15,12,9,... find the common difference and the nth term.
2. If 3x-1, 2x+2 and 2x-1 are in Arithmetic Progression, find value of x.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
1. Common difference is 3. Assuming we start with the first term denoted a%5B1%5D+=+15, we can write a%5Bn%5D+=+15+-+3%28n-1%29 (after some practice you'll be able to instantly find an expression for the nth term, then simply change n to n-1 or n+1 to satisfy the sequence).

2. If they are in arithmetic progression, then

a%5B2%5D+-+a%5B1%5D+=+a%5B3%5D+-+a%5B2%5D

%282x%2B2%29+-+%283x-1%29+=+%282x-1%29+-+%282x%2B2%29

-x+%2B+3+=+-3

x+=+6.