SOLUTION: Find the 1st term of the arithmetic sequence with 11th term −1 and 21th term 7.

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Question 927791: Find the 1st term of the arithmetic sequence with 11th term −1 and 21th term 7.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formulas.
d, common difference
n, term index
a, first term a%5B1%5D.
a%5Bn%5D=a%2B%28n-1%29d.
Use this formula and make two linear equations in the variables, a and d.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the 1st term of the arithmetic sequence with 11th term −1 and 21th term 7.
t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d

t%5B11%5D+=+t%5B1%5D+%2B+%2811+-+1%29d 

-+1+=+t%5B1%5D+%2B+10d

10d+=+-+t%5B1%5D+-+1______d+=+%28-+t%5B1%5D+-+1%29%2F10 ---------- eq (i)



t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d

t%5B21%5D+=+t%5B1%5D+%2B+%2821+-+1%29d

7+=+t%5B1%5D+%2B+20d

t%5B1%5D+%2B+20d+=+7 ------- eq (ii) 

t%5B1%5D+%2B+20%28%28-+t%5B1%5D+-+1%29%2F10%29+=+7 ------- Substituting %28-+t%5B1%5D+-+1%29%2F10 for d in eq (ii)

t%5B1%5D+%2B+2%28-+t%5B1%5D+-+1%29+=+7+

t%5B1%5D+-+2t%5B1%5D+-+2+=+7 

-+t%5B1%5D+=+7+%2B+2

-+t%5B1%5D+=+9

Term 1 or t%5B1%5D+=+9%2F%28-+1%29, or highlight_green%28t%5B1%5D+=+-+9%29 

You can do the check!! 

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