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
:
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k = 5
a(17) = 11 + 11(17-1) = 187
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:
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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