SOLUTION: 2k+1,5k-3,7k-2 find the value of k and 17th terms

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Question 1088206: 2k+1,5k-3,7k-2 find the value of k and 17th terms
Found 2 solutions by rothauserc, Edwin McCravy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
a(1) = 2k +1
a(2) = 2k+1 +d
a(3) = 2k+1 +2d
:
5k-3 = 2k+1 +d
1) 3k-d = 4
:
7k-2 = 2k+1 +2d
2) 5k-2d = 3
:
equations 1) and 2) are 2 equations in 2 unknowns - we can solve them by substitution
:
solve equation 1 for d
:
3) d = 3k-4
:
substitute for d in equation 2
:
5k -2(3k-4) = 3
5k -6k+8 = 3
k = 5
:
a(1) = 2(5) + 1 = 11
:
use equation 3) to solve for d
:
d = 3(5)-4 = 11
:
*********************************
k = 5
a(17) = 11 + 11(17-1) = 187
********************************
:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Oh crap!! The other tutor already did it for you!
I was only going to tell you the steps so you could do 
it yourself!  I wish the other tutors would do more of
that!  This is what I was going to tell you to do.
I like to teach students how to do their homework, not do
it for them.  You've heard the old saying "Give a man a
fish...".  But, oh well!



1.  Solve the equation for k:



That's the first thing you are asked for.

2.  Substitute the value you obtained in step 1,
for k in 2k+1 to find the value of the first term 
a1 = 2k+1.

3.  Substitute the value you obtained in step 1,
for k in 5k-3 to find the value of the second term 

4.  Subtract the result of step 2 from the result
of step 3 to get the common difference d.

5. To find the 17th term, substitute n=17, a1d = what you got
in step 2, and d = what you got in step 4.

Edwin
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