SOLUTION: g(1)=−19 ​ ​g(n)=g(n−1)+6 ​​ Find the explicit formula for g(n).

Algebra ->  Sequences-and-series -> SOLUTION: g(1)=−19 ​ ​g(n)=g(n−1)+6 ​​ Find the explicit formula for g(n).      Log On


   

Question 1089065: g(1)=−19
​
​g(n)=g(n−1)+6
​​
Find the explicit formula for g(n).
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
Thus defined function g(n) represents/describes the arithmetic progression with the first term -19 and the common difference of 6.


Therefore, the general formula for n-th term is


g(n) = - 19 + 6*(n-1),   n = 1, 2, 3, . . . ,


or, which is the same,


g(n) = (-19 - 6) + 6n = 6n - 25,  n = 1, 2, 3, . . .

Solved.


On arithmetic progression, see the lessons
There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".