SOLUTION: Determine the number of terms in an arthmetic sequence with t3= -17.5 and t10= -52.5. the final term in the sequence is -147.5

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Question 993264: Determine the number of terms in an arthmetic
sequence with t3= -17.5 and t10= -52.5. the
final term in the sequence is -147.5
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the number of terms in an arthmetic
sequence with t3= -17.5 and t10= -52.5. the
final term in the sequence is -147.5
t%5Bn%5D%22%22=%22%22t%5B1%5D%2B%28n-1%29d

Substitute n=3 and t3=-17.5

t%5B3%5D%22%22=%22%22t%5B1%5D%2B%283-1%29d

-17.5%22%22=%22%22t%5B1%5D%2B2d

Substitute n=10 and t10=-52.5

t%5B10%5D%22%22=%22%22t%5B1%5D%2B%2810-1%29d

-52.5%22%22=%22%22t%5B1%5D%2B9d

Now we have a system of equations:

system%28t%5B1%5D%2B2d-17.5%2Ct%5B1%5D%2B9d=-52.5%29

Solve that system and get t1=-7.5, d=-5

the final term in the sequence is -147.5

Substitute t1=-7.5, d=-5 and tn=-52.5
in the same formula

-52.5%22%22=%22%22-7.5%2B%28n-1%29%28-5%29

Solve that and get n = 10

Edwin