Question 412077: Hello, can somebody please help me with this question I don't understand it
The 8th term of an arithmetic sequence is 25 and the 20th term is -11. Find the first term of the sequence and the common difference and use those to write the general term.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The 8th term of an arithmetic sequence is 25 and the 20th term is -11. Find the first term of the sequence and the common difference and use those to write the general term.
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Equations:
a + 7d = 25
a + 19d=-11
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Subtract and solve for "d":
26d = 36
d = 18/13 (common difference)
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Solve for "a":
a + 7d = 25
a + 7(18/13) = 25
a + 126/13 = 325/13
a + 126/13 = 262/13
a = 199/13 (1st term)
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General term:
a(n) = 199/13 + (n-1)(18/13)
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Cheers,
Stan H.
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Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! Hello, can somebody please help me with this question I don't understand it
The 8th term of an arithmetic sequence is 25 and the 20th term is -11. Find the first term of the sequence and the common difference and use those to write the general term.
The other tutor's answer is wrong.
__, __, __, __, __, __, __, 25, __, __, __, __, __, __, __, __, __, __, __, -11, __, ...
The general term of any arithmetic sequence is the formula
for the nth term which is
an = a1 + (n - 1)d
Substitute 8 for n:
a8 = a1 + (8 - 1)d
a8 = a1 + 7d
Substitute 25 for a8
25 = a1 + 7d
a1 + 7d = 25
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an = a1 + (n - 1)d
Substitute 20 for n:
a20 = a1 + (20 - 1)d
a20 = a1 + 19d
Substitute -11 for a20
-11 = a1 + 19d
a1 + 19d = -11
Now we have the system of equations:
a1 + 7d = 25
a1 + 19d = -11
Solve the first one for a1
a1 = 25 - 7d
Substitute (25 - 7d) for a1
(25 - 7d) + 19d = -11
25 - 7d + 19d = -11
25 + 12d = -11
12d = -36
d = -3
a1 = 25 - 7d
a1 = 25 - 7(-3)
a1 = 25 + 21
a1 = 46
So a1 = 46 is the first term of the sequence and d = -3 is the common
difference.
So the arithmetic sequence is:
46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, -2, -5, -8, -11, -14, ...
The general term is found by substituting a1 = 46 and d = -3 in the
formula for the nth term:
an = a1 + (n - 1)d
an = 46 + (n - 1)(-3)
an = 46 - 3(n - 1)
an = 46 - 3n + 3
an = 49 - 3n
That's the general term.
Edwin
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