SOLUTION: if S2 = 10, S10 = 2 then what is a1, d (Arithmetic Sequence)

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Question 1092278: if S2 = 10, S10 = 2 then what is a1, d (Arithmetic Sequence)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Using a for the first term and d for the common difference...

S(2) = a + (a+d) = 2a+d = 10

S(10) = a + (a+d) + (a+2d) + ... + (a+9d) = 10a+45d

So we know
2a%2Bd+=+10
10a%2B45d+=+2

Multiply the first equation by 5 and subtract the second equation to eliminate variable a, then solve for d.

10a%2B5d+=+50
40d+=+-48
d+=+-48%2F40+=+-1.2

The common difference, d, is -1.2. Plug this value into one of the earlier equations to solve for a.

2a%2B%28-1.2%29+=+10
2a+=+11.2
a+=+5.6

The first term, a is 5.6.

Answers: first term is 5.6; common difference is -1.2.