Question 1039312: Find the value of k and 17th term of each of the following arithmetic sequence.
1. 7k+2, 4k+3, 2k+6
2. 2k+1, 5k-3, 7k-2
3. 7k+2, 5k+4, 4k-5
4. 3k+7, 2k-5, 6k-2
5. 2k-7, 6k-2, 8k+4
Please help me, i can't answer this and i feel awful about it.
Please teach me how to do one, explain the process. Advance thank you tutors.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! the nth term of an arithmetic sequence is defined as
:
Xn = a + d(n-1), where a is the first term and d is the common difference
:
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1) 7k+2, 4k+3, 2k+6
a = 7k+2
:
we have two equations in two unknowns
:
4k+3 = 7k+2 + d
2k+6 = 7k+2 + 2d
:
simplify each equation by combining like terms
:
3k + d = 1
5k + 2d = 4
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solve first equation for d
:
d = 1 - 3k
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now substitute for d in second equation
:
5k + 2(1-3k) = 4
5k + 2 -6k = 4
-k = 2
k = -2
:
using first equation
3(-2) + d = 1
-6 + d = 1
d = 7
:
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k = -2
d = 7
a = 7(-2) + 2 = -12
X17 = -12 + 7(17-1) = 100
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:
problems 2 - 5 are solved in like manner
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