SOLUTION: For an arithmetic sequence, find t(n) if: a. t(3)= 6.5 and s(8)=67 b. t(4)={{{ 6/sqrt(5) }}} and s(5)= {{{ 6sqrt(5) }}} Sorry, I really don't know where to start!! Please w

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Question 1006190: For an arithmetic sequence, find t(n) if:
a. t(3)= 6.5 and s(8)=67
b. t(4)= and s(5)=
Sorry, I really don't know where to start!!
Please write explanations if you can!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
check for the formulas in your book; but t is for term and s is for a summation. You have arithmetic sequence and series. This help is for your part (a).

t1+(n-1)d=tn, excuse the poor subscripting; and you have t1+(3-1)d=6.5.

Next facts give you s=(n/2)(t1+tn) but I really should show this to you better as
, and you were given the value of the summation,
.

You will have two equations in the two unknowns and d.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

For an arithmetic sequence, find t(n) if:
a. t(3)= 6.5 and s(8)=67
b. t(4)= and s(5)=
Sorry, I really don't know where to start!!
Please write explanations if you can!




_______ ------ eq (i)









 ------------ eq (ii)

 ----- Substituting 6.5 - 2d for  in eq (ii)



67 - 52 = 12d

15 = 12d

, or 



 --------- Substituting  for d in eq (i)











 ------ Substituting  for d, and 4 for  in equation of an AP

 









Apply the same concept to b. 

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