SOLUTION: the second term of an arithmetic sequence is 7, the sum of the first four terms in the arithmetic sequence is 12, find the first term and the common difference

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Question 892169: the second term of an arithmetic sequence is 7, the sum of the first four terms in the arithmetic sequence is 12, find the first term and the common difference
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
General term of the sequence, a%2B%28n-1%29d;
a = first term
n = index of the term
d = common difference

Your final term used in the series is n=4 for the expression a%2B3d.
The term at n=2 is a%2Bd=7.

The sum of your first four terms is %284%2F2%29%28firstTerm%2BlastTerm%29,
%282%29%28a%2Ba%2B3d%29=12
%282%29%282a%2B3d%29=12
2a%2B3d=6

Solve the system
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system%28a%2Bd=7%2C+2a%2B3d=6%29
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Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
S = ½(a + an)n
S = ½(2a + (n-1)d)n
an = a + (n - 1)d
S = ½(a + an)n
S = ½(2a + (n-1)d)n
12 = 4a + 6d
7= a + d
a=15
d=-8
a12 = 15 + 3*(-8)
a12=15-24=-9
a12=-9
S4 = ½(2*15 + (3)*(-8))4
S4=2*(30-24)
S4=12


15,7,-1,-9=22-10=12