SOLUTION: Hello, my name is kevin i need help with this 2 questions; Write an equation from the nth term of the architmetic sequence. Then find a10. 15. -2,5,12,19... 16. 13,9,5,1... P

Algebra ->  Graphs -> SOLUTION: Hello, my name is kevin i need help with this 2 questions; Write an equation from the nth term of the architmetic sequence. Then find a10. 15. -2,5,12,19... 16. 13,9,5,1... P      Log On


   



Question 1009259: Hello, my name is kevin
i need help with this 2 questions;
Write an equation from the nth term of the architmetic sequence. Then find a10.
15. -2,5,12,19...
16. 13,9,5,1...
Please say answer to both problems and all work
thanks

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences.
15.
-2,5,12,19...
For this sequence, if we add 7 to the first number we will get the second number,if we add 7 to the second number we will get the third number, and so on.
It means, the common difference (the difference between any two consecutive terms}}} is d=7
The d-value can be calculated by subtracting any two consecutive terms in an arithmetic sequence.
d+=+a%5Bn%5D+-+a%5Bn+-+1%5D
if a%5Bn%5D=19 and a%5Bn+-+1%5D=12, then
d+=+19+-+12
d+=+7
and your sequence will be
-2,5,12,19,26,33,40,47,54,61...
.
the nth term of the arithmetic sequence will be
a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d+.......where n is any positive integer greater than 1
then 10th term will be:
a%5B10%5D+=+-2+%2B+%2810+-+1%297+
a%5B10%5D+=+-2+%2B+9%2A7+
a%5B10%5D+=+-2+%2B+63
a%5B10%5D+=+61

16.
13,9,5,1...
d+=+a%5Bn%5D+-+a%5Bn+-+1%5D
if a%5B2%5D=9 and a%5B1%5D=13, then
d+=+9+-+13
d+=+-4

the nth term of the arithmetic sequence will be
a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29%28-4%29+
a%5Bn%5D+=+a%5B1%5D+-4+%28n+-+1%29+
then 10th term will be:
a%5B10%5D+=+13-4+%2810+-+1%29+
a%5B10%5D+=+13-4+%289%29+
a%5B10%5D+=+13-36
a%5B10%5D+=+-23